If your bunny’s testicles have dropped and you have a rabbit savvy vet who recommends neutering him at this age, then you could go ahead and do it, but if it makes you feel more comfortable to neuter him later, you could wait another few weeks.
You didn’t say if your female is spayed or not. You definitely have to keep your bunnies separate, and they shouldn’t even be in side by side cages, since rabbits have been known to mate through cages. And if your female isn’t spayed, you need to be aware that a male can still impregnate a female for a few weeks after his neuter, so they have to be kept separate for at least a month afterwards. But before you can truly bond your rabbits, your female will need to be spayed as well as having your male neutered. So if she hasn’t been spayed and if she is old enough, you should schedule that surgery too. Besides the fact that she will need to be spayed before bonding can be attempted, spaying her will eliminate the chance of uterine cancer.
Your male bunny may act a little differently right after his surgery, with all the fluctuating hormone levels, but he should still be the same, sweet bunny.