Ellie-May moved from cot to bed at about 20 months. Mostly because we found out we were expecting Jack and needed her cot for him, and I really did not want her to feel as if the baby was 'taking' her cot so I wanted to make trhe switch and give her enough time to settle before I was due.
She was already in her own room, but we made a big deal of taking her to buy a big-girls bed, and then started by putting her in it for her daytime nap. We left her cot up for 1 day in case of a complete meltdown, but we never needed it.
She was completely adjusted within a few days and we always told her that if she wanted us she should call us into her room rather than just getting out of bed and coming to find us, and she still does it now. Although now, we are trying to encourage her to get out of bed instead of shouting to us, as she now shares a room with Jack!
Good luck!
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