Hi,
I would definitily recommend to take the train. You have only to change once from Munich to Amsterdam. While our daugther is a little bit younger, we tried train and car. She definitly prefered the train. We try to avoid commuter trains, and try to choose trains which are empty. Playing around with her, feed her when she is hungry and not when there is a parking lot saves a lot of hassle.
If you rent a car, most rental companies also rent car seats. However, since your are never sure whether the car seat was in accident involved, I understand that you want to buy your own seat. We got our car seat from
http://www.spielemax.de/, other options would be toys'r'us or baby walz.
757DUD