Moving to Toddler Bed

What age did your child starting using a toddler bed? I know some people skip toddler beds and just go to a twin but I want to move my 13 month old to a toddler bed because she will stay sleeping on a mattress just not in her crib. I think a twin would be to high up for her. Also- do toddler beds use the same mattress as a crib or do I need to buy a new one? Thanks for the input!