Many years back a buddy owned a Volkswagon Kombi bus - one of those with no protection in front of you. We always kidded him, "In an accident, you will get there first!"

If you put your child on the handlebars in front of you - the child will "get there first."

In a rear carrier (or a trailer/buggy) the child is still very vulnerable, but it would have to be better than putting the kid up front.

Also - when I carried papers as a kid I tried looping the bag over the front bars because it was handier. I found that the added weight up high at the front made the bike unstable and quirky handling, so I switched to carrying the bag on the rear carrier. Even a rear mounted child seat will change the characteristics of the bike, but they usually sit lower than the saddle so it should be no worse than if you wore a back pack of similar weight.

If I had to make the choice I would lean toward a hybrid bike with a trailer (maybe with some extra cushions to support a one-year old) - just personal preference . . . . .

RE: Helmets for infant? Yes, many models for infants/toddlers. I sold many Giro & Bell helmets, many other brands available.