A programmatic companion piece by Bachlund, reflecting the inverted and logical-illogical world of the sequel. The music uses syncopation and chromaticism to represent the mirror-world theme.
Achieving clarity in the rapid, unpredictable shifts between registers is the primary technical task.
Comparable difficulty and character — good candidates for what to learn next.
Alice - Though the Looking-Glass is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6.
You should be comfortable at Henle level 4 — meaning you can already play level 3–4 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Alice - Though the Looking-Glass lasts about 3 minutes.
Alice - Though the Looking-Glass is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Alice - Adventures in Wonderland by Gary Bachlund, Ballade and Fugue in D major by Gary Bachlund, Alice's Humoresque by Gary Bachlund — see the full similar-pieces list on this page.