Is eating dairy and eggs, but no meat okay?

I'm 13 and recently I've been coming to the realization at how horrible animal slaughter is.. so I want to become a vegetarian. I can go without meat - when I see people preparing it, it makes me sick. But one thing that is hard for me to give up... cheese, milk and all that. Those products aren't related to animal killings? Or are they? Please tell me, because I adore dairy products, and I can't see them as bad.. tell me if they are..and can I be vegetarian without banning them from my diet? Thanks in advance and sorry for the stupid question.