Byerly’s Waltz is a classic example of American frontier-era piano music. It is marked by simple, balanced periods and a traditional accompanying left-hand texture.
Work on achieving a clean, detached sound in the right-hand melody against the steady left-hand accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
Byerly's Waltz 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 Byerly's Waltz lasts about 3 minutes.
Byerly's Waltz 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.