Percy Wenrich, a composer famous for ragtime, shows a more sentimental side in this parlor piece. The composition is built on predictable four-bar phrases and a standard accompaniment pattern.
The left hand needs to maintain a very steady, light alberti-bass accompaniment to let the melody breathe.
Comparable difficulty and character — good candidates for what to learn next.
By a Garden Gate 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 By a Garden Gate lasts about 3 minutes.
By a Garden Gate 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 Believe Me, If All those Endearing Young Charms by Irish Folk Music, Blue Moon by Lee S. Roberts, Arroz con leche by Wannes Vanderhoeven — see the full similar-pieces list on this page.