This is a guitar-influenced piano arrangement of the famous Irish folk melody often attributed to Thomas Moore. The arrangement features decorative arpeggiated figures typical of 19th-century salon repertoire.
The primary challenge is managing the phrasing of the melody against the flowing arpeggiated accompaniment.
Comparable difficulty and character — good candidates for what to learn next.
'Tis the Last Rose of Summer is rated Henle level 4 of 9 — intermediate repertoire, roughly ABRSM grades 5–6. In the RCM system it corresponds to about level 6.
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 'Tis the Last Rose of Summer lasts about 4 minutes.
'Tis the Last Rose of Summer 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 'O sole mio by Eduardo Di Capua, Belle of the Ball by Leroy Anderson, Broadway Melody by Nacio Herb Brown — see the full similar-pieces list on this page.