Long time lurker, first time poster.
There are some nice tweeter sleds new to the market- so good deals will be hard to find, but that new Yamaha Sno-Scoot is a mid size 200cc- great option for that 8-10 age group.
Also Polaris is doing their Indy evo. Likely for a little bit older demographic than your daughter- but it's a 550fan with a slightly shrunken, lowered chassis.
If you're looking for cheaper/used sleds- can't go wrong with an old 250 Bravo or 377 Citation.