Harry J. Lincoln was a prolific composer of marches and novelty piano pieces. Bo-Peep is typical of his accessible style, featuring simple melodies set against a persistent march-like accompaniment.
Practice the transitions between the melodic phrases to ensure a seamless and light performance.
Comparable difficulty and character — good candidates for what to learn next.
Bo-Peep is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 3.
You should be comfortable at Henle level 2 — meaning you can already play level 1–2 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 Bo-Peep lasts about 3 minutes.
Bo-Peep 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 Blaze of Honor by Harry J. Lincoln, Blumenwalzer by Léon Jessel, Bluin' the Blues by Henry Ragas — see the full similar-pieces list on this page.