M. Etta Hollister's piece is a pedagogical-style character piece focusing on basic keyboard facility. It uses straightforward harmonic patterns to create a pleasant and accessible listening experience.
At Henle 2 this is a beginner-level piece, where steady coordination between the hands is the main hurdle. The main demands: a true singing tone, with the melody floating above the accompaniment; Alberti-bass accompaniment kept quiet and even under the melody; and precise articulation — the difference between crisp and blurred is the piece.
Keep the alberti-bass left-hand figures soft and even so they do not overwhelm the right-hand melody.
Comparable difficulty and character — good candidates for what to learn next.
A level or two down with the same spirit — ideal if this piece is still out of reach.
Where this piece's skills lead: slightly harder works making similar technical demands.
Edelweiss 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 Edelweiss lasts about 2 minutes.
Edelweiss 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 Cuckoo by Arthur Foote, Es ist bestimmt in Gottes Rath by Gustav Lange, Es ist bestimmt in Gottes Rat by Gustav Lange — see the full similar-pieces list on this page.