Any male/female combo can live together indefinitely if you are willing for them to breed and produce young constantly. Most people prefer to keep their bucks (rabbits and goats) separate so they can control when the females breed and produce young. Otherwise up to you.
If your goats are year round breeders your doe is going to get worn out. She won't get a break between kids. The buck doesn't care if she needs a break. You also have to think about the babies. If there are doelings the buck doesn't care how old they are either. They can cycle as early as 8 weeks and believe me - he will find a way.
If they're not year round breeders it will be much simpler.
Buck won't hurt the kids unless he wants to breed the does and they are in the way (wanting to nurse) then he will try to drive them away from the doe.
Bucks can also try to nurse the does. Plus, one buck will wear out one doe. I would suggest looking at getting a second doe or whether, that way when you need to separate mom and baby the buck won’t be lonely. I usually prefer three to two though, on the off chance someone dies you’re not in such a bad spot.
One question though we forgot to ask - are these just pets or do you want to breed them? If these are just pets without any thoughts of breeding, consider castrating the buck. Then they can stay together with no problems. An additional benefit is that a wether does not develop the bad bucky tendencies - butting, bad smell during rut, and pushiness. A wether makes a sweet pet.