E.M.
uhmmmmmm I'd wait a long, long time to put her on the bike in anything but a pull behind trailer. and even that is months away.
we had a trailer and even with that, my pediatrician strongly suggested we wait until they were a year old AND we could find a properly fitting helmet. The problem, just like in cars, is the weight of her head is disproportionate to her body. Thus, stopping is an issue, even at slow speeds - her neck just cannot control the forward momentum of her head. And a crash, shudder to think about it.
also, are you going to be able to keep the bike in balance with her shifting all over the place? that was one of the reasons we went with a trailer. the other was that we felt there was less likely to be a crash that would affect them and the trailer had a full roll bar if we did crash.
while I know people who did put their infants in a trailer, we would not. If the child is not big enough to be forward facing in the car (1 year AND 20# when mine were young), they are not ready to be sitting upright, facing forward, in any kind of vehicle (car, bike, trailer, etc).
use a stroller for a few more months. she will grow up quick enough to do all these fun things.