We did a long car journey (4 days with overnight stops, then 3 days on the way back) with our firstborn when she was 5 months old. One of us sat at the back to entertain her, equipped with the usual army of toys, colourful pictures, baby food etc. etc.
It went fairly well, she had no big problems. Whenever she wanted to move more than it was possible inside her safety seat, or was breastfeeding time, we stopped for a break. (She already started to eat some solid food at that time, but was still being breast fed a couple of times a day.) For a 2 months old, I guess this would cause even less trouble.
One of our friends did a similar journey at that summer, with a somewhat bigger baby. They also shared the back seat with the baby. They travelled mostly during the night, so their baby slept through most of the travel.