Our city guidelines say to wait until one year in a trailer and wear a helmet, but my brief research has told me that pulling a smaller baby in a secure sling is probably safer than driving them places.
This leads me to believe that you're considering "utility" biking on local streets and not just "recreational" biking on park paths.
I always respect and defend parental choice even when I don't like the choice that's being made. With that said, be extremely conscious of the parameters and the risks of this decision. Don't make this choice because of an Internet article or someone's opinion on this forum, even though many of us here avidly support biking. Make this decision carefully for yourself. And for the record, a student I taught years ago lost an infant daughter at 14 months--riding in a car, baby in fastened car seat. The young mother was tired after a late night, heading to daycare at 5am, and pulled out in front of a Dodge truck going 45mph, a speed allowed in most suburban areas. Driver error pure and simple, and the error was the mother's. Hard to live with. I know the family well.
Ask yourself this question and see how you respond--If you were rear-ended, and your baby died, would you still feel you made the right decision?
Rear-end and other car/bike accidents are not as common as non-riders assume. But the potential loss is much higher for the baby than the bike rider. I can't stop, turn, or dodge as quickly with a trailer. Also, if I am rear-ended by a vehicle at a reasonable speed, I might be thrown clear after impact. A child trailer will be destroyed. Furthermore, if you are riding at a time when you feel that lights on the bike/trailer would be helpful, then you are statistically increasing the likelihood of an incident--dark being one of the leading factors in car/bike incidents that is not correlated to rider stupidity, e.g. alcohol, riding the wrong way, etc.
I am willing to ride in traffic that non-riders feel is unsafe. I am willing to ride in traffic that my bike-commuting wife feels is unsafe for her to ride. My safety expectations for pulling a child trailer would be much higher than any of those--lower posted speeds, lower traffic volume, etc. Why? Because even in my mostly bike-friendly suburban town, drivers make mistakes that I'm willing to face myself but unwilling to subject my child to. I can't answer my own posted question in the affirmative outside of a two-mile radius surrounding my home/neighborhood. Posted speeds = 25mph, traffic volume is 2-3 cars passed per mile.