I would take the current cover off if there is a chance of Koko getting onto it. If she gets on it she may be in real trouble. When we had our pool put in we were told if we weren't going to use a safety cover then don't use anything because those are dangerous. If a person or animal gets on it they could get wrapped up and drown very easily. Our pup likes to run across the safety cover and it sinks just enough for her to have some water to play in. I can't wait until this summer to get her swimming!
This is a very good point. Those tarps can be death traps.