Sometimes the stress causes an adrenaline release which prevents the system from processing the anaesthetic.
I'd suggest you go with her, and ideally stay with her while she has a premedication as this is what they'll use to "prep" her for the anaesthetic. If the premedication has a good effect, usually the GA induction goes a lot smoother. If you think having you there would help reduce her stress levels I'd discuss it with your vet prior to booking her in.
We used to have to do this with certain dogs, where the dog and owner would sit in the consult room, and we'd sedate with the owner there, and do the minor op we needed with the owner in the room.
Big ops, owners stayed for premedication, and induction but left once taken through to theatre.
Never had to do it with rabbits, but I know of other practices that used to have to do this.
Also having her booked in for a day when they have no dogs booked in for ops is a good idea, as they're often loud and stressy which makes prey species even more stressed out.
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