what do you plan to do with the boat? Miami Airport is near NW 36th St.
Anyway, we've been up the Miami River to NW 17th St. and beyond, but I don't think we got close to the airport, and all the bridges (I think) are drawbridges. We tried going as far as we could, but that was several years ago and I've forgotten just where the river ended for us.
There is a marina, Airport Marina, 2669 NW 33rd St. Miami, FL 33142 305-634-1686 - very close, it seems. Try calling them.