There would be several problems with that scenario. A passenger on a motorcycle has to lean into curves along with the driver. That would be extremely difficult with a small child in a seat. Not to mention that motorcycles are open, which means in the case of an accident, there is an extremely high chance that a child will get seriously injured or killed, much more so than in a car. There is also a chance of the child getting hit by flying debris. If you want to even consider this, you may have to get a sidecar. That would probably be the only semi-safe way to transport a small child on a motorcycle.

Best bet, just buy a small, fuel efficient hybrid car.