There's been plenty of discussion about this in Rec and Family, including the thread above.

I personally put my daughter on a bike at around 10 months, using a front-mounted bobike mini. She was very large for her age, and looking back on it, I should have started her much sooner. She absolutely loved riding on the bike. The only issue with the bobike mini is that there is no lateral support, meaning when they fall asleep, and they will, they will slump forward and to the side. She was never at risk of falling out, but it looked so uncomfortable that I would hold her up with one hand, not always easy.

I would personally be comfortable riding with an even younger child, though I would have to research the options a little more. The dutch have some excellent options, but they can be difficult to get in this country.

Everyone has their own comfort level though. I am a confident rider, going so far as to take my Electra Amsterdam with daughter in the bobike through some singletrack trails on multiple occasions.

Even if I accepted that I was putting her at more risk than say, driving her in a car, I would argue that the experience more than makes up for it.