Do rabbits have a period?

Chances are it's a phenomenon called "red urine". This happens when a rabbit eats a high-protein food such as alfalfa hay. If your rabbit is eating alfalfa hay or a lot of rabbit pellets, switch her to a Timothy hay based diet with pellets as only a supplement and eliminate any alfalfa hay. But do get your bunny spayed. Rabbits are horribly prone to uterine cancers which cause bleeding from the vagina. At her age I doubt that that's what's causing her symptoms,; but it will almost certainly happen as she gets older. So get her on Timothy hay, use pellets as a supplement only and get her spayed.

Rabbits don't get periods as they are induced ovulators, meaning they don't have fertility cycles. But rabbit urine can vary in color from clear to yellow to white to red or orange. You should definitely be able to tell the difference between red/orange urine and blood. This is likely caused by something in her diet so if there are no other symptoms don't worry.

The other possibilities (though it definitely doesn't sound like these are the case) would be a UTI or something similar or ovarian cancer. A urinary tract or bladder infection would definitely be accompanied by other symptoms, so if this is just occasional reddish urine don't worry about it. Ovarian cancer can cause bleeding and is exceedingly common in unspayed rabbits (up to 80 percent), but it's extremely unlikely that that would be the case at six months old. Just make sure to get her spayed before she's a year or so, as doing so completely removes the risk.

For now she's likely fine. If you notice any other symptoms (blood, straining to go to the bathroom, drinking a lot more or less) then you could call your vet, but there's nothing to worry about at this point!