Rogers wrote various pedagogical and salon pieces in the early 20th century. This work offers a sophisticated harmonic palette while maintaining the gentle character of a lullaby.
Balancing the accompaniment chords so they do not overpower the expressive melody is the primary goal.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse in A major is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6. In the RCM system it corresponds to about level 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 Berceuse in A major lasts about 4 minutes.
Berceuse in A major 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 Bridal Song by James Hotchkiss Rogers, Bossa Nova by Serban Nichifor, Blumengruss by Carl Bohm — see the full similar-pieces list on this page.