Welcome here! I am really sorry to hear about Peter. I can definitely understand your concerns. Being put under anesthesia is risky, for humans and animals alike. There is always the possibility that something might go wrong. Do you know what happened during the teeth surgery? Was it an error on your vet’s part, or did you have no explanation? Another thing to keep in mind is age. The older a bunny is, the more risky the surgery might be. Usually with young bunnies, they can be put under and recover easily. If Peter was older, he may have had something else wrong with him that you and the vet were not aware of and he could not handle anesthesia. If you are very concerned, or if your girl is over two years old, I’d recommend you do blood work before the surgery to make sure there are no underlying health issues.
Are you confident with your vet’s ability? Is this the same one who saw and operated on Peter? It’s very important that you see a rabbit-savvy vet for rabbit care. A dog and cat vet may agree to see your rabbit, but unless they are experienced with a high success rate, I would not allow them to operate. Anesthetizing rabbits is different from cats and dogs. If you are not sure, go ahead and cancel the appointment and do some research in your area for another vet. The House Rabbit Society has a list of questions you can ask to determine the “rabbit-savviness” of a vet.
Spaying is a necessary surgery. It is not only for the behavioral benefits. Females have a very high risk (80% approximately) of developing uterine cancer by the age of 3 if not spayed. Their bodies are designed to make lots of babies in a very short time frame. Because of this, cancer develops very quickly. A surgery to remove cancer will be riskier (and more expensive!) than a “preventative” surgery to spay.
As far as your other concern, medicating after the surgery, she will be groggy for at least the first 24 hours, and in most cases, they are relatively “low-key” for the first 3-5 days. Is there someone who can help you give her meds? What works for us is my husband will hold her back-end still, while I open her mouth and administer the meds. Sometimes it’s easier with a helping hand.