Good luck!!!
We just switched DD to a big bed at 13 months, while she had SA, teething, independant sleep issues, 2-1 transition and some major changes in our household. And she is a slow adjuster.
And now, one month down the track, she is giggling herself to sleep which she has never ever done before. You can do it
She only tried to get out a couple of times, for once I think doing this younger may have been on our side, she isn't the greatest climber yet
However, she did have the SA - I think if you just keep on putting her back if she climbs out, she will get the message, it has worked for all our other sleep issues.