A Bayfield 25 would be a nice, gentle intoduction to sailing. With one small child you'd have a pretty good setup for a while.. learning the 'ropes' and it's an easy boat to singlehand (essentially) with one person primarily child-minding.
Non toddlers are actually easier to deal with than toddlers. They sleep more, more content to sit/lay in one position for a while, and can't yet get themselves into potentially worrisome places. Add a good leecloth to one of the settee berths and he/she'll sleep contentedly and safely while you sail along. Babies that age don't get bored, aren't scared of 'new' situations and as long as their needs are met there's rarely a problem.
Once they're more mobile the challenges get bigger, but are totally manageable with some forethought. Our 3 year old granddaughter is totally content to play in the V berth while her parents are doing a local beer-can race - they holler 'tacking' below and she scoots to the new low side and continues to amuse herself. She's been sailing since she was a week old.
Starting at this young an age is truly best... they grow up with it and don't know any different. Introducing 6, 8, 10 year olds to sailing is much more difficult. They can be frightened, bored, confused by the environment... kids that grow up in it - it's just normal.
Typically it's a bigger issue for the parents than for the child.
As kids grow they need more space, and you have a built-in rationalization for the occasional bout of '2-foot-itis' as you look for a larger boat. With luck they'll grow to love it and carry on as adults, as our son has done....
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)