Echo might be the closest First Nation counterpart in the Avengers.
Update: Katana will be featured in Green Arrow's title during the Outsiders war. Whether she will survive or not is hard to judge.
In an interview with Jeff Lemire with Newsarama, it appears that Green Arrow wn't be the leader of the Justice League United, but he will be a mentor to younger members Stargirl, Supergirl, and the First Nations girl, who Jeff has still not revealed. So the leadership will be either Adam Strange, Hawkman, Animal Man, or Martian Manhunter.
Now, if only we learn about the future whereabouts of Vibe and Simon Baz. I just hope Simon could have joined JLU. Vibe, on the other hand, I'm still not a fan of.