An XA2 isn't a bad choice. The only disadvantage I can think of is no built-in flash - an external flash makes it somewhat bulkier than other "true" P&S cameras out there. Depending on what she likes to take pictures of, that might be an issue.
For size and still very good picture quality, with autofocus and an integrated flash, I would suggest an Olympus Stylus Epic - going for $100 or less on eBay. It's very compact - I think the smallest P&S I've seen, and is a decent performer, as long as the fixed 35mm lens isn't a problem. On the downside, I had one break in a pocket while on vacation (reason unknown), but I seem to be in the minority there. Also, in a zoom, the Stylus 80, 120, or 150 are also good choices - I now have a Stylus 120, it *hasn't* broken in my pocket, and it's still quite good.
Otherwise, on the total P&S front, I've heard very good things about the Canon Sureshot Classic 120 - so much so that I've bought one myself and it just arrived the other day. The advantage it has is they go cheap (it cost me about US$35 on eBay for very good/near mint condition), it has a decent lens (but a bit slow - it's f/4.5 - 10.6), and it has +/- 1.5 EV exposure compensation (not incremental, though, it's all or nothing one way or the other if you decide to use it). Lots of positive reviews if you search around for it.
Of course, the disadvantage to "true" P&S cameras vs. the XA2 is that most P&S are limited to DX-coding only for film speed (other than the exposure compensation of the Classic 120), so if at some point you wanted to teach her about pushing/pulling, or the limits/flexibility of film, the XA2 might be a better choice.
Anyway, just some thoughts...