William F. Sudds's composition is a charming example of late American romantic piano music designed for the pedagogical market. It is distinctive for its lush use of the sustain pedal and lyrical melodic arcs.
Practicing the wide-span arpeggios in the left hand is essential for achieving a fluid, non-percussive sound.
Comparable difficulty and character — good candidates for what to learn next.
Autumn Song (Op.88) is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 5.
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 Autumn Song (Op.88) lasts about 3 minutes.
Autumn Song (Op.88) 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 Brook Song by William F. Sudds, Bon Ton by William F. Sudds, Berceuse by Emile Jaques-Dalcroze — see the full similar-pieces list on this page.