Johann Friedrich La Trobe's variations reflect the salon style popular in the early 19th century. The piece is characterized by melodic ornamentation typical of the period's lighter keyboard repertoire.
Focus on clarity of ornamentation and evenness of touch in the faster variations.
Comparable difficulty and character — good candidates for what to learn next.
12 Variations on an Andante is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 4.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 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 12 Variations on an Andante lasts about 7 minutes.
12 Variations on an Andante 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 18 German Dances and Esoccaises by Franz Schubert, 18 German Dances and Ecossaises by Franz Schubert, 18 German Dances and Esoccaises, by Franz Schubert — see the full similar-pieces list on this page.