We have been biking with our kids since they were very young. The general rule is that they be able to hold their head up well.
There are infant helmets on the market, and I've found that a small cushion placed behind the baby's back helps to keep the helmet from forcing the baby's head forward. The maker of our trailer, WIKE, sells a "helmet relief cushion" that has loops for the harness straps to fit through. It makes the positioning of the head and neck much more comfortable! Because our kids have been wearing helmets since before they can remember, they don't argue with our rule of always wearing a helmet when riding in the trailer or on their own bikes. I definitely suggest starting early for that reason, as well as for safety.
We started with short rides and built up. Our kids are now 2 1/2 and 4 and are happy on long rides, as long as there is a park stop along the way!
If you're interested in riding with someone, let me know!