This intimate miniature is a classic example of amateur parlor music from the Victorian era. It features a simple, heartfelt melody set against a balanced homophonic accompaniment.
The player must emphasize the melodic top notes within chords to achieve the required cantabile quality.
Comparable difficulty and character — good candidates for what to learn next.
'Twas under a Willow Tree 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 'Twas under a Willow Tree lasts about 2 minutes.
'Twas under a Willow Tree 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 Für Elise by Ludwig van Beethoven, At Bedtime, TH 70 by Pyotr Tchaikovsky, Albumblad, EG 109 by Edvard Grieg — see the full similar-pieces list on this page.