This is a salon galop typical of 19th-century parlor music meant for light entertainment. It is distinguished by its rhythmic drive and characteristically simple, buoyant melodic contour.
The primary challenge is maintaining a consistent, brisk tempo while executing the rapid articulated bass figures.
Comparable difficulty and character — good candidates for what to learn next.
Belle of Ireland Galop 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 Belle of Ireland Galop lasts about 3 minutes.
Belle of Ireland Galop 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 Alexander's Ragtime Band by Irving Berlin, Waltz in D-flat major, No. 1 by Frédéric Chopin, 12 Variations on 'Ah vous dirai-je, Maman' by Wolfgang Amadeus Mozart — see the full similar-pieces list on this page.