This piece by the Danish composer Fini Henriques is a quintessential example of the late-romantic miniature form. It is characterized by its warmth and simplicity of expression.
Focus on the phrasing to ensure the music breathes naturally in the lullaby style.
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 5.
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 Billedbogen by Fini Henriques, Berceuse sur le nom de Gabriel Fauré by Maurice Ravel, Berceuse by Rudolf Friml — see the full similar-pieces list on this page.