This arrangement of the traditional Irish air is representative of the pedagogical and parlor literature popular in the American mid-19th century. It explores the emotional resonance of the melody through simple but expressive variations.
The challenge is to maintain a seamless, vocal line throughout the melodic variations without resorting to harsh accents.
Comparable difficulty and character — good candidates for what to learn next.
'Believe Me If All Those Endearing Young Charms' (Op.58) 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 'Believe Me If All Those Endearing Young Charms' (Op.58) lasts about 4 minutes.
'Believe Me If All Those Endearing Young Charms' (Op.58) 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 Berceuse by Dora Pejačević, Candlelights by Bix Beiderbecke, Amar... Nocturno para piano by Felipe Villanueva — see the full similar-pieces list on this page.