Dripping Springs is nice and lots of native Texans still live out that way. Good people. Given the distance from Austin and the lack of ability to travel there easily she's still in a good area. But going into downtown/South Austin... it's a complete shithole. Also, APD doesn't patrol dripping springs, it's wayyyy too far outside their jurisdiction - she would have a more local police department there, This would fall under Hayes County and not Travis County (We call it Travesty County) which is also a good thing. I would not stress AS much.
My wife and I chose to move WAY north of that city for a reason, and honestly it's not quite north enough for my taste.
But rest a bit easier knowing she is in a relatively good/nicer area and the locals/natives there are pretty upstanding for the most part. And she doesn't need to rely on Austin PD or Travis County for any assistance.
However, I would encourage her to get comfortable around a firearm and to have one on her persons for protection if at all possible/willing when dealing with Austin Proper/Travis county.