This is from 楽しいムーミン一家. You can watch the full dialogue here starting from 2:35 if you need more context. The part I'm asking about begins around 3:25.
Basically, winter is coming so Snufkin is planning to go on a journey as usual. Moomin doesn't want to part with his friend so he asks Moomin Papa if he can go together with Snufkin. Papa says:
Snufkin loves to be alone. For him it needs to be a solitary journey no matter what.
To which Moomin replies:
The overall message is undoubtedly "I know that" but what does だって add here? My guess is that it means "I know that better than anyone else" but I'm not sure... It doesn't seem to match the dictionary definitions.