The SR22 is a good pistol. It's highly functional, quality, and also quite affordable. The downside is that you're getting a gun with nearly subcompact barrel length and resulting sight radius. That doesn't mean it can't be accurate, but it's a certainty that accuracy will be more difficult than with many similar guns.
If the SR22 fits her way better than anything else, buy it! If she loves it, she'll probably put in the work to become proficient with it, and will be a better shooter as a result of that process.
But if she's more of a casual shooter, there may well be better alternatives...that could include rimfires like the SW MP22 or Ruger 22/45 (two that have impressed me), or a bigger centerfire.
The simple answer is to buy her what she'll enjoy. <---Underlined is an easy (and always correct) answer that can be difficult to sort out from your perspective. The SR22 is an excellent gun; but it doesn't come without it's own set of shortcomings, depending on the expectations of the shooter. I love and own the Ruger MK3 22/45, but I'll probably buy an MP22 and SR22 in the near future. I like all three guns. I'd prefer the 22/45 above the other two.
"The Future is Unwritten"