I think 1 kid, not 2.
I have a 13 year old Civic, so probably comparable to today's Fit. I can do 2 kids no problem, but not 2 kids + dog, because where would the dog go?
In the case of the Fit, you could do 2 kids + dog, but no stuff.
Camping got really tight for us with the 2nd kid, and we are pretty minimalist. You definitely couldn't camp in a Fit with 2 kids and a dog.
But, how often do you camp and when will you really have 2 kids?
We were given a minivan and it is awesome for camping, but without that gift we were going to go with one size bigger than Civic in order to camp with 2 kids and not be miserable. YMMV. Also depends on ages- baby hardly takes up room (except for giant carseat), but my kids are 10 and 7 and have legs, so we can't stuff things on the floor of the back seat any more.