This is a quintessential example of early 20th-century novelty piano writing with a jaunty, syncopated character. Its melodic phrasing is highly reminiscent of the Tin Pan Alley era.
Focus on precise, percussive placement of the chords to capture the novelty-style rhythm.
Comparable difficulty and character — good candidates for what to learn next.
'Zis' for You, 'Zat' for You! is rated Henle level 2 of 9 — beginner repertoire, roughly ABRSM grades 2–3. In the RCM system it corresponds to about level 2.
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 'Zis' for You, 'Zat' for You! lasts about 3 minutes.
'Zis' for You, 'Zat' for You! 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 Big Blonde Baby by Fred Fisher, Bach-anh-114 by Johann Sebastian Bach, Bach-bwv-anh-114 by Johann Sebastian Bach — see the full similar-pieces list on this page.