What would it be called (because they wouldn't be based on Looney Tunes), who would be on the team, and what would their power be?

One would be a descendant of Pebbles and Bam Bam's kids, and be the super-strong member.
The descendant of Yogi and Cindy would be the resourceful member of the group.
I suppose Gazoo would be the team overseer/instructor, given his punishment and time-travel experience.
The descendant of Penelope Pitstop and Peter Perfect is perfect for portraying speed.
Johnny Quest's successor would be the thinker.
The rest could be fair game, given how many existing supers there already are.

6283585
Well there are no Humans on the Loonatic so why would there be any on the Hanna-Barbera version?

Because roughly half of Hannah-Barbera's characters ARE human?
And some of those humans are actual people, like Mike Tyson. Kinda complicates things.

6283369
If I think of something I'll come back to it.