Our three-year-old still co-sleeps with us. Is it time for her to sleep in another room?

Yes, I would imagine. My nephew is 2 years old and now has his own bed. You can probably do this in stages. - Start off by having a cot in the same room and once she is off to sleep, move her to the cot. That way she would be close to you in case she wakes up, easing your fears as well. - Once she gets familiar to the cot, move the cot to a different room. Hopefully, it goes smoothly for you :)