I would get her swimming lessons, honestly, and a foam pad trainer to help keep her safe in the meantime. You can get one for about 10 bucks at Walmart, OP makes them. There are several pads in it, and as the child's swimming skills increase, you can remove them, one by one, until they no longer need the help. Unlike floaties or rings, this also keeps the child in a natural, horizontal swimming position.
Floaties & rings can come off &/or become deflated. They also force the body to be vertical, & in an unnatural position for swimming, so kids automatically start swimming with their bodies & limbs in the wrong positions when they wear them too much. You will have to correct that, on top of teaching them how to actually swim.
Of course, no swim aid is a substitution for proper supervision.
Your DD is more than old enough to learn how to swim & she needs to learn that life skill ESPECIALLY because you have a pool in your backyard.