Your diet sounds fine. It is most likely coccidia. This is very common in young bunnies that come from pet stores. The vet will test the fecal sample and prescribe medication that should clear it up quickly.
It does take awhile to manifest, sometimes a couple months. What may happen is the rabbit breeder (who is usually aware of the issue!), medicates all of the rabbit water with a low-dose of medication, just enough to suppress the parasite, but not eradicate it. I’m not sure why they do this, maybe they believe it’s too expensive and time-consuming to daily medicate every rabbit individually, so they just dose everyone. This “fixes the problem” temporarily. Once the baby bun goes to the pet store and then home with a new family and is away from that water source, the parasite has a chance to return, which is when you would start to see symptoms.
A baseline exam with a new rabbit is always a good idea, and the vet will be able to answer any specific questions you may have.