Personally I'd want to keep on eye on my infant instead of sticking him/her in back or even in the front passenger seat of a car where I can't see whether he/she is choking or being jerked around by the bumpy road. That goes for any vehicle whether it be car, bicycle, or otherwise.

SImultaneously, I'd also want to travel more slowly and carefully with a newborn baby than I would be traveling otherwise; Which also goes for any vehicle, car, bicycle, etc.

Now let's consider a few facts:
-Cycling with the infant in front view will be difficult to achieve.
-Neither driving or cycling is the epitome of safety. Even if suitable support for infants are more easily attained for cars I would not want to risk subjecting an infant to a car crash at speed, nor would I want to strap an infant to two wheeler which will topple in a crash.
-Cycling is generally only 4x faster than running and 2x faster than skating. If we are cautious and take a slower pace then how much faster will cycling with baby really be than these alternatives? Maybe 2x faster than running or the same as skating?

Therefore, why not use a jogging stroller? Many come with head and neck support specifically approved for infants, you can keep watch, if you use a pair of inline skates then you might not even lose much speed compared to cautious cycling, and you will gain a lot of safety (especially if you can combine it at all with public transit, which is the safest way to travel). Might even be quicker than either cycling or driving since you won't have to transfer your infant into a stroller before entering shops.