What type of mold? “Toxic Mold” is not safe for Humans or Animals, because you breathe it in. Exposure to mold is not good. Here are some types of categories for dangerous mold and what they can cause (in humans):

Allergenic Mold— Contains an allergen that can effect people with low immune systems, like those with Asthma

Pathogenic Mold— This mold is capable to cause diseases, although a lot of healthy adults can resist infection, although it’s dangerous to sick/young/old people.

Toxic Mold— (black mold is under this group) This mold produces toxins that can be as minor as causing allergies or as serious as causing cancer.

There’s also several other categories. I don’t know what mold you have, but I’d do some research and look into it, to make sure you have no “bad” mold. If it is bad mold I personally wouldn’t want to risk housing my rabbit in that room

Yes, black mold is toxic. I would suggest replacing the gyproc.

I would also suggest wearing protective masks/clothing to do so. Not just dust masks, respirator models.

Please be very careful, I’m allergic to mould and if there is mould a friend cleans the place for me with white vinegar, I am allergic to penicillin which is mould, the other night I ate a bit of cake, I noticed it was a bit green underneath. (Perfect for Halloween but not to eat) I had to get some special tablets from the doctor to be on the safe side, the best thing to do really would be to get your ceiling repaired, it is a fungus plant so it will spread, good luck.