How to keep my cat out of my daughter's room?

We just recently got a cat a little over a week ago. We are trying to keep him out of my daughter's room because she has her guinea pig in there and he likes to jump on the table where the guinea pig is which scares her guinea pig. I have tried keeping her door shut but that doesn't really work because her door handle is broke and you can just push the door open. Also the cat has already figured that out. When I see him walking towards her room I have tried clapping my hands or making some kind of loud noise but he just turns around and stares at me like I'm crazy lol. I was thinking about getting a baby gate but I figured he could just jump over it. We tried "boundary spray" with out previous cat and that didn't work for her. I know every cat is different but I don't want to waste my money on it if it doesn't work. Anyone have any ideas what I can do?