This post is for parents with babies around one year old that are trying to figure out how to bring their precious cargo along for the ride. Obviously, this is just what worked for me and what I was willing to do. Consider your skill level, equipment, road conditions, etc., before attempting any of this at your own risk. In Tacoma, we also have a helmet law that applies to all riders, so you may have to deal with that in your area, too.
I've personally had success with two methods when my kids were tiny. The key was neck strength: kids need to be strong enough to hold their head up firmly when helmeted in order to handle the acceleration/braking force. Keep in mind that the helmet makes their head more top-heavy, so this is a bit different than kids riding without a helmet in a jogger stroller.
My Kid #2 was a slow grower and, early on, couldn't keep her head up comfortably with the helmet in the bike trailer. When she was about 11 months old, I would put her carrier carseat in the bike trailer facing forward. I lap-buckled the carseat in the trailer (Burley d'Lite) and left the carrier handle up like a roll bar. She was then buckled into the 5 point carseat harness as usual and did not wear a helmet. This was good for slow riding (maybe 10mph) with gentle acceleration and braking (barely faster than a jogger stroller). She would often fall asleep and I could slow pedal the neighborhood for an hour on quiet streets. Some additional visuals here.
My Kid #3 was small but very strong. He started riding in a Yepp Mini stem-mounted kid seat at age 8 months, with a helmet. It was awesome: he was perched right in front of me and could see what I could see. I could see him point at things and tell him what they were called. I think this led to him speaking well at an early age. The downside is that those seats are hard to get fitted properly so that the parent rider isn't pedaling knees-out to avoid hitting the seat. They don't fit perfectly on every bike. I purchased my Yepp seat (and a larger one later on) from G & O Family Cyclery in Seattle, which is the go-to place to find a wide assortment of family bikes in the greater Tacoma area. Here is my son on one of his first rides. That Lazer helmet was the smallest I could find and he still needed the hat to make it snug.
There are also cargobikes/boxbikes with boxes or buckets on the front or back that are perfect for carrying small kids or carrier carseats. We had a Madsen "bucket bike" when Kid #2 was 14 months and she sat in it with a lap buckle and helmet, along with her 3yo sis and 3yo cousin. I've seen other parents buckle carseats into the bucket and still have room for another small kid or groceries.
This is certainly not an all-inclusive post, just a summary of my experience with my own children. The one thing I will add pertains to the upfront cost of family bikes, trailers, kid seats, etc. Most of the name-brand gear holds up well and retains its value over time. The bucket bike was a about $1200 new, and we used it 5 days a week for 2 years, then sold it for $600. That was an excellent value to me (both physically, mentally, emotionally!) and just part of our transportation budget during that time.