This waltz is an arrangement of the popular music hall song by the same name, reflecting the light-hearted salon style of the late Victorian era. It features a straightforward, tuneful melody supported by standard accompaniment patterns.
The primary challenge is keeping the left-hand accompaniment light and rhythmic to allow the melody to sing clearly.
Comparable difficulty and character — good candidates for what to learn next.
"My Old Dutch" Waltz 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 "My Old Dutch" Waltz lasts about 3 minutes.
"My Old Dutch" Waltz 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 Autumn Waltz by Stephen Foster, At Twilight by Rudolf Friml, 'A robba fina! by Eduardo Di Capua — see the full similar-pieces list on this page.