If I remember correctly, buzzing is a hormonal sound? Wick never buzzed, but I believe it is normal for unfixed rabbits.
It’s good that you had your rabbit checked by a vet early on! A great first step and it’s good to build that rapport with a vet from the beginning.
I will highlight two things that stand our:
1) Make sure the buzzing is an intentional sound and not the result of nasal blockage or something stuck in the lungs. Wick would sort of squeak when he had snuffles way back when. He was a very vocal rabbit, but then I realized it was because his nose was always stuffed. Now he’s silent, haha.
2) You mention another rabbit, so would you plan to bond them? If so, I would recommend the safest route of keeping these two separate until both are fixed. Also it gives your baby some time to get used to you and the new environment. After some time, you can progress to prebonding and bonding. This site provides a basic guide for this in the BUNNY INFO section at the top bar.
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.