In reply to klara.m:
Have you got a spare adult to leave with your kid at the bottom of the crag? If not, then we found that bouldering was by far the best option when our kids were that age. If anything goes wrong with your little one while you're on lead, responding to it quickly is very difficult if both of you are attached to ropes etc. Although I would say we are definitely at the relaxed end of the parenting spectrum, we only tested this once, it was so disastrous we said never again, and that was before our eldest was mobile.
If you've got a spare adult then most of the Peak crags are great with kids. We've always taken enough clothing to keep them warm and something to provide shelter if it's really sunny. A couple of toys are useful, but from what I remember of little ones they were quite happy eating grass/rocks/insects and so largely entertained themselves.
Ours are now 4 and 6 and love a good day at the crag, it definitely gets easier as they get older.
