I agree she is probably ready to start potty training, and the other posters have great ideas on how to keep the diaper on.
I have another suggestion of something to do while trying those other tips. If she pees, make her help clean it up. My 16 month old son has had lots of fun making messes with his bottles/sippy cups [tipping it over and watching the formula drip out, pushing the nipple down into the bottle and then pouring the liquid out, unscrewing the top and pouring it on the floor, and then spreading it around with his hands] and about a month ago, I started to make him help me wipe it up. I would tell him "no, we don't______" "you made a mess, let's clean it up."
I gave him a wipe, and held his hand and wiped it up with him. I kept doing this until he got the idea, and then I started to tell him "you made a mess" and to "wipe the mess" "clean it up" without my help. Now, only a month later, he is very careful about not tipping his bottle or sippy over. He even puts it up on the table by himself when he is ready to move onto something else. Actually, this approach has nearly eliminated his throwing food off of the highchair as well. Obviously when he cleans something he doesn't do it very well and I still have to wipe up what he missed, but I don't mind since he is helping and learning a lesson. When he throws Cheerios off of the highchair however, I don't help other than if he misses some, and I'll tell him "honey there are more over here, please pick them up" "thank you".
Anyway, I think if you tried this with your daughter, she would eventually connect her peeing with the mess and the dirty sheets that she has to help clean up. When she wakes up with wet sheets and no diaper on, I would say "Honey you took your diaper off again and now the sheets are all wet. We will have to change them." And then tell her "if you don't want to pee in your diaper, you can pee on the big girl potty like Mommy does" and show her how to sit on the potty.
She might not get it at first but if you keep it up I bet that she will either stop taking her diaper off or start peeing in the potty. But even if she doesn't, at least she is learning to help clean up a mess that she made