Hiya....
I am a nurse working at a vet surgery and I can tell you now that rabbit mortality under GA (general anesthetic) can be quite high even for simple procedures. Spaying your rabbit will reduce the chances of cancer (as neutering any animal will) but it is debateable whether it will have much of an effect on her behaviour. Spaying rabbits is usually recommened more when you have a doe and buck housed together to stop unwanted litters.
The individual you spoke to was probably a receptionist so before you make any decisions ring your surgery back and ask to speak briefly to a qualified vet or nurse - if that isn't possible, then book a consult to see a vet and take your rabbit along with you to get a full health check carried out (to make sure it is in good enough health to even start considering a GA).
Ideally, if you decide to push ahead, try and find an 'exotics' vet to do the op - these vets have trained specifically with smaller species in mind and will have far more confidence and experience with rabbits.
Its a matter of getting proper professional advice and weighing up the pros and cons. A GA and an invasive op like a spay is a substantial risk for a rabbit, but as long as the animal is young, healthy and has the right surgeon on the case then it stands a good chance of coming though.
Hope that helps.
Lulu