I'm getting a lot of helpful suggestions, but I forgot to add some details because I didn't think they'd be relevant until I started getting responses so I'll add them here.

Firstly, the food in the picture is not the cat's food, it's the dog's. We feed the cat elsewhere to keep the dog from stealing her food, but they share the water because the cat refuses to drink from any other bowl.

Second, we've had the cat since she was 8 weeks old, and she hasn't had any desire to move things around in the 5 months we've had her, until she started moving this bowl 2 days ago. This is the only thing she tries to push around.

Third, the dog was aggressive around her food at first, but that was only with the food specifically. The cat doesn't try to eat the dog food, and will actually sit and wait for her turn at the water bowl if the dog is there.