It was no trouble for us, we did it at 2 years 3 months. I have absolutely no idea if any of these following things helped or if we were just lucky, but this is what we did...
We talked about it for a while beforehand (like you have) and so she seemed very prepared/excited.
We put the bed up a couple of nights before she went in it so she saw exactly where she would be sleeping (it was in a different bedroom too), and let her sit on it in the day.
We took her to Dunelm to pick a duvet cover (honestly that was a waste of time though, she was so grumpy and I ended up picking it myself).
I told her that the bed is just like the cot- once you are in it, you are in it for the night. I let her make requests for books, a magazine and some cuddly toys and I put them at the bottom (it's a full single so plenty of room) and told her she can play on the bed, but not get out.
First night we waited until she was really tired, let her stop up late. She was still excited though so couldn't sleep. She climbed out after about an hour and was traipsing about upstairs. I just put her back in each time and kissed her and reminded her that if she wants to play, she has to do it on the bed (she nearly always takes a while to sleep unless she's particularly tired).
After a couple of nights, she was absolutely fine. She gets out sometimes before sleeping, but usually only to retrieve a book or a cuddly toy from the floor. She sleeps just as well if not better than in the cot. In the mornings we hear her wake up in a really good mood so I know she slept well.
Twice she has cried out once and then when I looked on the video monitor (which we had anyway didn't buy it specially or anything) she was just climbing back in. Don't know if she fell out or what, but she was straight back asleep.
Good luck. I think you have to prepare for a few nights where it is a bit of a novelty, but your LO is pretty much same age as mine and they do have a good understanding of what is happening which made it a really smooth transition for us. x