This is a characteristic cradle song by the English-born American composer Horace Wadham Nicholl. It features a lush, rolling accompaniment pattern that supports a serene, vocal-like melody.
The primary challenge is maintaining an even, rhythmic 'rocking' motion in the left hand while shaping the melodic line.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse 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 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 Albumblad by Oskar Merikanto, Berceuse by Georges Marty, Berceuse by Adolf Gutmann — see the full similar-pieces list on this page.