I moved with a 14 month old, and again, with a 2yrold and an 8mth old. Pack as much as possible during nap time, then, during the day when your little one's up, put a bunch of toys in a box, or turn a box on it's side to make a little cave, kids LOVE boxes! This should keep him/her out of your hair. As for what to pack and when - pack the small things, anything sentimental - books, DVD's and CD's, ornaments, winter clothes, the spare stroller, extra bedding, anything you feel you can live without. Even the kitchen, pack up as much in there are you feel you can do without. Maybe you could prepare enough meals to keep you and your family going for the next couple of weeks and freeze stuff, then pack most of the kitchen up. Pack away most of your little one's toys, only leave the ones that are used the most. I have the Evenflo exersaucer, and if that's the one you have, it folds relatively flat without being dismantled, and will fit into the original box without the toys attached. You can pack it last and unpack it and set it up first and keep your little one occupied for a while (my son loved it, but my daughter hated it with a passion). Break down anything you can, if your wardrobe is a flat pack, buy a wardrobe box and hang all your clothes in there, then break down your wardrobe and get that out of the way. Only leave the basics, and most of the basics you'll have will go straight on the truck as is - your sofa, mattress, the kitchen table (though you can go without that for a couple of days if needs be, so maybe, if it can, break it down a day or two before the move date). Maybe move your baby into a pack and play for a few days before the move so that you can break down her crib. Find out if your moving company provides a specialist removals service for your TV, especially if it's a plasma or LCD TV (the vast majority are now), if not, make sure that you pack the TV well so that it's not damaged in the moving process.
If you're worried about packing anything, particularly the bigger of the baby's toys, consider packing them into the car and taking them around the your new place before the move, that way, you can have them ready and waiting when you get there for your little one.