The room with mold isn't safe, for anyone. After the landlord cleans it & there's no other signs of mold anywhere in the room, i would start on it. That way you can work on it little by little. You can take a certain project a week at a time that way you dont overdo it. If you wait until your furthet asking, it will be a little harder cause your belly will be in the way & you may have less energy.
It's not safe for you to beto be in the room or probably even in the house with mold. Is the landlord coming to fix it soon? If so I would say wait until they do come fix it then start, but that seems like a lot of work you have to do and it may be uncomfortable for you to do all of that while you have a bigger pregnancy belly. It's really up to you when you would like to start, though.