It sounds like your vet is knowledgeable about rabbits, but that his receptionist is not, and just gave you the standard line she would tell anyone whose dog or cat is having surgery. But just to be sure, it might be a good idea to clarify this and make sure that the vet didn’t tell her that. There is no need to fast rabbits before surgery.
In my experience, the rabbit will go home late that day and not have to stay overnight. You should take some hay and veggies with you because they like to see that the rabbit is eating afterward. When she get home, she will likely be sleepy from the pain medication. She shouldn’t need any more the first day, but they will give you medication for the next 2 or 3 days. If she had any multi levels in a condo or x-pen, you should make sure that she stays on the ground level and is not jumping around, which could possibly open up her incision.
Here is the page that Dana Krempels wrote about surgery: http://www.bio.miami.edu/hare/opcare.html
I’m very sorry about what happened to your first rabbit. I hope that Missy sails through her spay and recuperates very quickly.