Beethoven and Alice in Wonderland

Perhaps Carroll would have been listening to music of this style if he had been born 100 years later. Carroll was, after all, very conservative in his mathematics teaching. Although new mathematics were being rapidly developed in his time, he still used Euclid's books as his guide, and was very meticulous in going through it. He wrote a play called "Euclid and his Modern Rivals" which asserted that nobody can write a better geometry textbook than Euclid.

Thus, I think he would be a rather musically conservative person as well. This sonata movement is an example of relative musical conservatism in comparison to what was being produced in Carroll's time, the middle-to-late 19th century. By then, the late Romantic period was underway, and composers like Beethoven were considered old music.
It was the opinion of some intellectuals, though, like Aldous Huxley, that good music ended with Beethoven, and although there are no sources available on Lewis Carroll's music tastes, I believe I can assume he shared the same opinion as Huxley.