This Berceuse by Joseph Arthur Mann is an accessible, student-level work focused on developing a singing tone. It captures the lullaby aesthetic through simple, effective rhythmic repetition.
Pay close attention to the articulation of the rocking accompaniment to ensure it does not overpower the melody.
Comparable difficulty and character — good candidates for what to learn next.
Berceuse No. 1 is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 3.
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 No. 1 lasts about 2 minutes.
Berceuse No. 1 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 Berceuse Op.28 no1 by Anton Simon, Berceuse by Maurice Deffrennes, Berceuse enfantine by Georges Charton — see the full similar-pieces list on this page.