This piece by Charles Wely is a typical example of French salon music from the mid-19th century. It features a straightforward melodic structure designed to showcase a light, singing touch.
The technical focus is on managing the subtle dynamic gradations to create an atmospheric, soothing mood.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse 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 Berceuse lasts about 3 minutes.
Berceuse 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 Black Beauty by Duke Ellington, Berceuse by Rudolf Friml, Albumblatt by Moritz Moszkowski — see the full similar-pieces list on this page.