Parenting woes

My daughter hates tummy time. When I do it with her, she cries within a few minutes. Before that she will just lay there and suck on her hands. I put toys in front of her and she could care less. I rattle them for her and she loves it, but doesn't want to do it herself. I have toys hanging from her carseat and she looks at then all the time, but doesn't bat at them. In her excersaucer she loves when I play with the toys, but she won't. I encourage her to by batting things with her hands for her. It just seems like she doesn't care. If I put a rattle in her hands, she holds it for a little bit, but doesn't understand what it is.