It’s very important that rabbits are spayed, especially the girls. Intact girls have a big chance of developing uterine cancer by age 4, so the sooner Pepper gets spayed, the better. As Sarah mentioned, territorial behaviour is usually driven by hormones and she’ll calm down in a couple of weeks. I totally understand your worry about the procedure, but the risk of complications is low nowadays. Spaying is a big operation for a bunny, but vet science has improved a lot since people started to keep house rabbits. Luckily anaesthesia and surgery techniques have become so much better that it’s considered a safe procedure when done by an experienced rabbit vet.
My BF was also very hesitant to get our male Nethie Breintje neutered, because his neighbour told him scary stories about accidents during surgery. Breintje never had hormone troubles while he still lived at my BF’s place, but when Breintje moved into my apartment he got a massive hormone surge at age 2. It drove everyone crazy: it wasn’t fun to be in the same room with him anymore because he was so frustrated and angry about everything. He started to mount everything, not only his toys but also my craft projects. It’s not a fun surprise to pick up your knitting and to find out that he’s been at your ball of wool again :/ Luckily his neuter went really well, and he bounced back to health within 3 days. With girls this recovery period will be a bit longer, and they’ll get pain killers because it’s a bigger operation. We had a happier, calmer and more snuggly bunny within weeks, and despite our hesitations it was a great decision.
About vets: the vet needs to have a lot of experience with rabbits, because they’re considered to be exotic animals. Your regular cat&dog vet may not have the required specialty. Ask a vet how many spays/neuters they do on rabbits each year, and if the vet is a certified exotic pet vet. There’s a topic on this forum with links to webpages where you can find a certified vet, it’s called “Vet Resources”
There’s one way to spot a bad vet: if they advise you to bring Pepper in sober, run! Cats, dogs and humans have to be sober for an operation because we can vomit and this can cause asphyxiation. Rabbits can’t vomit, they have a one-way system only. They’ll also need that energy to recover from the procedure. A good vet will tell you to give her a good breakfast and to bring her favourite foods in for when she wakes up.
I know that there’s a lot to consider, but I’d advise you to get her spayed to prevent uterine cancers, and to help her with all those raging hormones. Hopefully you can find a rabbit savvy vet nearby!