There will never be a definitive answer to this question. Those of Mozart’s biographers who mention his sister Nannerl, generally take it for granted that she was a good player, but would absolutely not have been able to compose. I wonder how one can claim to judge a talent that never had the possibility of expressing itself. How can a seed that does not fall on ground where it can take root, ever grow to be a plant?

Only the Australian professor Martin Jarvis — renowned for his controversial theory that the Suites for solo cello were, in fact, composed by Anna Magdalena Bach, instead of her husband — has argued forcefully that Nannerl wrote music since childhood. Jarvis believes to have identified her “musical fingerprint” in the Nannerl Notenbuch, the music book used by both sister and brother to learn and play the harpsichord; some of the pieces in the book would have been composed by Nannerl herself.
This theory was categorically denied by the Mozarteum, based on objective evidence.
Let’s take care of the facts, then. We have few certainties regarding Nannerl’s musical aptitude but they are significant. We know that she was considered a virtuoso on the harpsichord. As a little girl she performed as a duo with Wolfgang in the international tours organized by their father, and in the announcements of concerts and newspaper articles she was named — and praised — first. An article in the “Augsburger Intelligenz-Zettel” of 19 May 1763 reads:
Imagine a little girl of eleven interpreting the greatest Maestros’ most difficult sonatas and concertos on the harpsichord, with great clarity, inexpressible lightness, skill and style. It was a source of wonder to many.
In a letter written on 21 June 1763 from Munich to his friend Lorenz Hagenauer, Leopold Mozart — their father — referred to the elector Maximilian III Joseph as having much regretted not being able to hear Nannerl in concert:
The prince twice said that he was sad not to have heard the young girl play: because, when we were at Nymphenburg, there was not enough time. It is true that most of the time was taken up by my son, who played solo […]. After her performance, Nannerl received the greatest applause, from both the prince and the duke. Each of them, when saying goodbye, asked us to come back very soon.
In Paris, a few months later (1 December 1763), Baron Friedrich Melchior von Grimm reported in “Correspondance littéraire, philosophique et critique” (a handwritten periodical that informed the aristocracy of cultural events):
Real prodigies are sufficiently rare to be worth speaking of when one comes across them. A Kapellmeister from Salzburg, by the name of Mozart, has just arrived here with two children who cut the prettiest figure in the world. His daughter, eleven years of age, plays the harpsichord marvellously and performs the longest and most difficult pieces with impressive precision.
In a letter to Frau Hagenauer of 1 February 1764, again from Paris, Leopold wrote:
My daughter plays the most difficult pieces by Schobert, Eckard and other composers, and interprets Eckard’s compositions, which are the most delicate, with incredible precision. The infamous Schobert could not hide his jealousy and made himself ridiculous not only in front of Eckard, who is a good man.
Incidentally, Johann Gottfried Eckard (1735-1809) and Johann Schobert (1740?-1767), German composers, were darlings of the Paris salons. It is not known why Leopold felt such resentment for Schobert.
In short, there are many letters in which Herr Mozart vaunts his daughter’s skill at the keyboard and the praise she received. The most relevant indications of the young musician’s talent, however, come from her correspondence with her brother. In a letter from Bologna dated 24 March 1770, Mozart addresses her: “Oh, you hard-working creature!”, because Nannerl had send him a “stolen” copy of some minuets by Michael Haydn. She had easily transcribed them from memory at the end of a concert. Later, from Naples on 19 May, Mozart wrote again:
I very much like the twelfth minuet by Haydn that you sent me; the basso continuo is peerless, without the slightest mistake. Please, try to do this sort of thing more often.
Probably spurred on by such affectionate praise, Nannerl tried her hand at composing a Lied and sent it to Wolfgang for his opinion. On 7 July 1770 he replied from Rome:
Cara sorella mia! [“My dear sister” in Italian]. I’m amazed to discover that you can compose so delightfully. In a word, your Lied is beautiful. You must compose more often.

What we really don’t know is what happened to that Lied, and if Nannerl listened to her brother’s exhortations and composed more; although we can be fairly sure that she didn’t because to write music that no one would ever play would de-motivate even the most determined of talents.
What’s more, it is difficult to imagine that Nannerl had specific knowledge in the field of composition: it would have been silly to instruct her in a career that she would never have been able to follow. Much more sensible, once she had grown up and was therefore no longer “usable” as a child prodigy, would be to make her teach the harpsichord, so that the money she earned could go to fill the family coffers and finance the study, travel and artistic promotion of her brother. Naturally Nannerl continued to play in public, but mostly (and certainly not by chance) she performed her brother’s compositions.
To conclude, we can be certain of one thing: due to circumstances, over the course of the years Nannerl Mozart’s musical talent, however great it was, gradually dried up and went to waste.