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.
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.