It is not in a fairy tale setting, then the story is as short and told with as much of his lighthanded (or, not always so*) sentimentality as the stories that are fairly and squarely fairy tales. In this sense, this tale is like The Girl with Matches.
However, the action is that a Jewish family in Denmark has the situation of having a daughter who wants to become Christian. Once she has heard of the sacrifice of Christ, of God coming down to die on a Cross and then Resurrection. Or rather, she has a Jewish family. And the problem in Denmark, we are talking 19th C., is that she is forbidden to get baptised against her parents' wishes. She never gets baptised.
Denmark takes the side of her parents against the side of what was considered its faith.
H. C. Andersen speculates that she was surely saved anyway. After all, she wanted to get baptised and was stopped by others. I am less sure. She should perhaps have put up more of a fight about it. Even though it is decades since I read the story and might be forgetting part of how much of a fight she did put up in the story. But what I am sure of is that Denmark was exaggerating parental authority.
There are TWO cases in which you are old enough to get baptised against your parents' authority, if they are Jewish and against it. One is if you are close to dying, as in the case Mortara. One is if you are old enough to know what you talk about and old enough to ask it - which means a minimum of seven years**, when it comes to receiving the Christian faith in an official manner independently of your parents.
I have complained that parental authority is attacked by Child Protective Services and by School Compulsion even against parents recalcitrant to send their children to school.
I have NOT complained that this draconic exaggeration of some parental authorities hasn't the full support of society.
Hans Georg Lundahl
Octave of Sts Peter and Paul***
* In some cases his sentimentality and concentration on how sad such and such a thing was goes amuck, and it is more Dostoevski than H. C. Andersen.
** Or just possibly 12. The words of St Thomas are these, as cited by New Advent:
I answer that, The children of unbelievers either have the use of reason or they have not. If they have, then they already begin to control their own actions, in things that are of Divine or natural law. And therefore of their own accord, and against the will of their parents, they can receive Baptism, just as they can contract marriage. Consequently such can lawfully be advised and persuaded to be baptized.
If, however, they have not yet the use of free-will, according to the natural law they are under the care of their parents as long as they cannot look after themselves. For which reason we say that even the children of the ancients "were saved through the faith of their parents." Wherefore it would be contrary to natural justice if such children were baptized against their parents' will; just as it would be if one having the use of reason were baptized against his will. Moreover under the circumstances it would be dangerous to baptize the children of unbelievers; for they would be liable to lapse into unbelief, by reason of their natural affection for their parents. Therefore it is not the custom of the Church to baptize the children of unbelievers against their parents' will.
III P. Q.68 A. 10 (cited after Newadvent site)
For having the use of free-will involves being able to sin mortally and to repent of sin, there the limit is 7. But for making matrmonial decisions about one's life, it is usually 12, and marriage also involves fulfilling certain physical actions, by which token boys marry earliest at age 14.
Here is what St Thomas has to say about age limits for marriage and betrothal:
I answer that, Since marriage is effected by way of a contract, it comes under the ordinance of positive law like other contracts. Consequently according to law (cap. Tua, De sponsal. impub.) it is determined that marriage may not be contracted before the age of discretion when each party is capable of sufficient deliberation about marriage, and of mutual fulfilment of the marriage debt, and that marriages otherwise contracted are void. Now for the most part this age is the fourteenth year in males and the twelfth year in women: but since the ordinances of positive law are consequent upon what happens in the majority of cases, if anyone reach the required perfection before the aforesaid age, so that nature and reason are sufficiently developed to supply the lack of age, the marriage is not annulled. Wherefore if the parties who marry before the age of puberty have marital intercourse before the aforesaid age, their marriage is none the less perpetually indissoluble.
Note especially objection 5 and solution to it:
Objection 5. Further, it is not included under any of the aforesaid impediments (50), and consequently would seem not to be an impediment to marriage.
Reply to Objection 5. The impediment arising from defective age, like that which arises from madness, is reducible to the impediment of error; because a man has not yet the full use of his free-will.
Suppl. III P. Q.58 A.5
I answer that, The age of seven years is fixed reasonably enough by law for the contracting of betrothals, for since a betrothal is a promise of the future, as already stated (1), it follows that they are within the competency of those who can make a promise in some way, and this is only for those who can have some foresight of the future, and this requires the use of reason, of which three degrees are to be observed, according to the Philosopher (Ethic. i, 4). The first is when a person neither understands by himself nor is able to learn from another; the second stage is when a man can learn from another but is incapable by himself of consideration and understanding; the third degree is when a man is both able to learn from another and to consider by himself. And since reason develops in man by little and little, in proportion as the movement and fluctuation of the humors is calmed, man reaches the first stage of reason before his seventh year; and consequently during that period he is unfit for any contract, and therefore for betrothal. But he begins to reach the second stage at the end of his first seven years, wherefore children at that age are sent to school. But man begins to reach the third stage at the end of his second seven years, as regards things concerning his person, when his natural reason develops; but as regards things outside his person, at the end of his third seven years. Hence before his first seven years a man is not fit to make any contract, but at the end of that period he begins to be fit to make certain promises for the future, especially about those things to which natural reason inclines us more, though he is not fit to bind himself by a perpetual obligation, because as yet he has not a firm will. Hence at that age betrothals can be contracted. But at the end of the second seven years he can already bind himself in matters concerning his person, either to religion or to wedlock. And after the third seven years he can bind himself in other matters also; and according to the laws he is given the power of disposing of his property after his twenty-second year.
Suppl. III P. Q.43 A.2
*** When writing this, I had not looked further than first line of the martyrology. But it is also St Maria Goretti in Nettuno, and St Thomas More in London! This goes both for signature and for previous footnotes.