I cycle with my 7 month old in a bike trailer. I bought a decent trailer with nice suspension and he is quite comfy back there. I have a little additional support to help keep his head and body from slumping too much while sleeping. I have the Chariot CX1 and love it.
You might check with your pedi and get his/her opinion on where your LO one stands, developmentally, in terms of readiness for biking. Also check with your local and state laws concerning kids and bikes. State law where I live specifically states the following. I suspect that most states are in the same arena as this.
1. If you carry children or other passengers inside an enclosed trailer or other device that will adequately restrain them and protect their heads in a crash, they need not wear helmets.
2. You may not carry any child between the ages of 1 to 4, or weighing 40 pounds or less, anywhere on a single-passenger bike except in a baby seat attached to the bike. The child must be able to sit upright in the seat and must be held in the seat by a harness or seatbelt. Their hands and feet must be out of reach of the wheel spokes.
3. You may not carry any child under the age of 1 on your bike, even in a baby seat; this does not preclude carrying them in a trailer.
Here is some helpful information regarding cycling and kids.
http://www.bhsi.org/little1s.htm
http://hea-www.harvard.edu/~fine/opi...dcarriers.html
http://www.ibike.org/education/infant.htm
Of course no one wants to put themselves out there and say 'go ahead and bike with your baby' but I think that if you do your research, have your child evaluated, purchase proper and appropriate equipment... then you can make the determination of whether or not you want to assume the risks.
I researched this topic to death and could add tons more. Let me know if I can help at all.
~kat