We also put our child on car seat when she is 1 month old. It was ok until when she is about 8 months when she struggle to get out of the car seat. She would cry when we put her in but after 3-4 times as we ignore her, she got use to it. Now, when we going out, she will climb on her car seat.
I think it is good to start as early as possible and need to be a little "cruel" to let them cry though it melts our heart. But after a few times, they will give up and sit in the car seat.
I notice that one of the reason why my baby cry after a while is because she wants to see outside. So we need to change the carrier to a car seat. Hope this helps.