Wirelessly posted (BlackBerry8703e/4.1.0 Profile/MIDP-2.0 Configuration/CLDC-1.1 VendorID/104)

If your doggie gets delivered to AA's freight facility, you have no problem: collect your baggage, pick up your car, and then drive to AA's freight building.

If your doggie is delivered to the in-terminal baggage claim, use the on-airport long-term lot. You can travel between the terminal and the lot, free of charge, via the AirTrain. Rent a luggage cart at baggage claim, and load your bags and the doggie (in his carrier) onto the cart, and take the AirTrain. If it is too much to take your luggage and the doggie on one trip to the parking lot, take the luggage first, stow it in your car, and take the AirTrain back to the terminal to collect the doggie.

And I second the recommendation that you first make sure that the doggie would not be subject to quarantine upon arrival in the U.S.