I have 3 girls - 11, 6 and 6 months. I let my oldest watch the younger two often, at least once a week or if I need to run errands. The most important thing to look at when making this decision is the child's maturity and responsibility. I know 18 years old "adults" I wouldn't let watch the dog! Make sure who ever watches your child knows what do in an emergency. It would be a good idea, if you're going to let her babysit often, to get her certified in child CPR. Your local Red Cross should offer classes and they are usually free. A first aid course might not be a bad idea either. These classes would be good for the whole family. If, heaven forbid, an actual emergency should occur, everyone will know how to respond and knowing what to do/expect helps everyone to remain calm. Make sure she knows the family plan in case of a fire, too. If you take these precautions, you'll be more at ease and your family will be much safer. If the other children are going to be home also, you may want to think about how they will react to the oldest being in charge. You don't want the oldest fighting with the other ones while she's taking care of your baby.
Another little tip - When I first started letting my oldest babysit, I started with maybe half an hour or so and gradually worked up to a few hours. You don't want to leave her and then have her decide she can't handle it or just doesn't want to any more. I also took the baby's monitor, one of those ones with the TV type monitor, and hooked it up to the VCR with RCA cables. I hid the camera end in the living room and didn't tell my daughter about it. This way I could see exactly how she handled the situation/responsibility. (I bought mine at K-Mart for $100.) These monitors have come in handy for several other situations too and it has turned out to be a very good investment. We also used it to catch the neighborhood kid who kept causing mischief outside our garage. If you have a mini DVR or camcorder, it would work also. At first I tried using the DVR, but it only records about an hour and you have to make sure the batteries are charged. This situation could also be a good opportunity for a lesson on the value of money if you wanted to pay her for sitting.