I would not put my child in anything that did not already have "foam" in it. I also do not think the auto-inflates are USCG approved for children unless they have changed the rules.
My first child was on board at 5 days old. He has more miles under him than most the people on this forum. A kid and the right boat is no big deal. Promise. I do think that learning the boat first before throwing Little Johnny aboard is a smart move. Not that it necessarily endagers the child, but it allows you and the spouse to get a better grip on how to sail and master working together without distractions.
Be aware, when sailing with kids, you are basicaly singlehanding (sailing solo). One will be pretty involved witht eh kids while the other is the primary captain. Ii am sure there are exceptions to hat rule, but I don't know them. A s such, it is important both you and spouse are proficient independently on the boat.
Also, teach your kid to swim ASAP. I'm not sure they're ever too young to start. That will relieve a lot of your concerns.
Sailing with children is all about attitude. It is not the baby's atitude, it is mom and dad's. You can make it work. Please don't sweat it. Just be cautious and safety minded, but learn to relax and have a good time. The relax and good time part is more about confidence in yourselves and your abilities on the vessel than the issues with the kiddo. And just a warning, the infant age is the EASY age. You put them, they stay. When they are two-three, that is where it really becomes interesting because they can climb over crib sides, up companionways, over combings, etc. The infant age is a piece of cake.
BTW, it is all worth it. Best decision we ever made taking our kids cruising and we leave again soon. Here's what you have to look forward to...
I could keep posting these for hours....