I don't know that there's a specific age by law for babysitting, but most places that offer babysitting classes require the kids to be at least 12. A lot would also depend on the kid's level of maturity, experience, common sense, how long she'd be sitting and when (I'd be more likely to leave my kids - when they were younger - with a 12yo for a couple of hours in the afternoon, rather than at night), the neighborhood, if the other parents are going to be available if there's a problem/question.
I'd also make sure that she's aware of what to do in various emergencies - and even ask that she take a babysitting class before she watches your kids.
There's no legal age limit on how old a child must be to leave him/her alone. It's a judgement call, but if something were to happen you would be liable. My two (11 & 13 now) have been staying home on their own under varying circumstances & times for several years. The younger one is more personally responsible (i.e. she can be left in the morning and I know she'll be ready for school and not miss the bus) but is more likely to be talked into letting some friends come over in the afternoon/evening. So I'm less likely to leave her for any stretch of time when that's likely to happen. Whereas my older one is more likely to lose track of time, not be ready, miss the bus, etc - but I know he won't get talked into something stupid.