Well, I would seperate them when the doe is 10 weeks (unless the buck starts humping her before that), then wait til she is at least 5-7 months (depending what size they are), breed them, wait until you are sure she's pregnant (can sometimes take the full month, but chances are extremly high when she cooperates and you keep them together for 3 days - if they get along), neuter the buck right away, reintroduce the buck 6 weeks after neutering (can be fertile that long), get rid of the kits with 8-10 weeks (or you'll have to seperate males from females again, and even after 5 years of breeding I still always get a second opinion when sexing the kits).
Anyway, do you already know what to do with the offspring? Be sure of that before breeding. (Just putting them on Craiglist isn't much of a plan). I sell what I can, the rest gets invited to dinner.
You know that breeding isn't always that nice, smooth experience, most time it is (depending on the breed, the line, the rabbits), but you can also end up with a heap of dead rabbits, or anything in between. It would be good to keep contact to the breeder where you have them from to have help if something happens, or for sexing the kits.
I wouldn't breed any rabbits that have genetical issues like pinched hips, teeth problems, fragile health, allergies, etc., that's just adding to the overall problem, many people are poorly prepared for vet bills.
Personally, I also wouldn't breed dwarfs or other breeds with semilethal genes where I can expect that 25% will wither and die, but that's just my preference.
Another point is space - they have one cage, do they still have enough room when you divide it and there are 5-10 more rabbits in there? I hope that's not one of those pet shop cages they sell here for rabbits (more suitable for hamsters or maybe guinea pigs). When I started I made hutches like my grandparents used for their meat rabbits, after a few days it was clear that was cruel and tore them down.
There are good reasons why pet rabbits are neutered, that hormonal behaviour often somewhat collides with what people expect of a pet. Some maturing bucks can be quite messy, spraying 2,3 feet wide and high.
Unspayed does have their issues too, what bothers me most are their mood swings when going through false pregnancys, but all that depends on the characters of the individual rabbits.
But have the buck spayed asap, I still get an oops litter now and then, and with the most recent one I simply can't figure out how they did it. Smarter than me, those critters.
Does your mom have experience with rabbits? That sure would help, and some points I mentioned would be moot. You have still a few months to plan a ahead, in the end, it's solely your decision how you proceed.
After having said all that: It sure is fun to have a litter of baby rabbits, they are so much fun and when handled a lot from the beginning can make very sweet pets. Just always be aware that you can't keep them all. Good luck
Oh, another version. That's not true, or can you link the study showing that? It's contrary to what I see every day. This whole cancer thing gets blown out of proportion and is used as generic argument for everything. Just because numbers keep being repeated over and and over because they fit some peoples agenda doesn't make them any more true.
But true, rabbits do have a higher risk for uterine cancer, I guess about 2-3 times the rate of humans (now, that rate more than doubled in the last 60-70 years), so in my opinion 20-30% will get some growths in their lives, but not necessarily dying of that. That "after 5 years 80% will die" is imho made up nonsense to propagate spaying.
I don't say that spaying is not a good idea for pet rabbits, it is, but using fake arguments discredits that, as if there were not a lot of good arguments...
Also the inbreed angle isn't as dire in rabbits as many think.