Importing Dogs from USA

[sandgrubber]

If I move, it will be at least nine months from now, and I will bring my three dogs.
No problems with my visas . . . I hold an Australian passport.
The dogs are another matter. Looks like there are six or eight vet checks that need to be completed on schedule and with the proper stamps, signed off by authorized people. No fun, but I can manage it. Then quarantine, no fun, but at least a bit less rigid than the equivalent in Australia.
Where I'm stumped is in putting the whole thing together. Should I be looking for a pet transport company to put the dogs on the plane and deliver them to quarantine? Or is it possible / better to arrange directly with the airline? If necessary, I guess I could drive across the US with the dogs and get them flown out of LA. The logistics of sending them from Florida seem pretty messy, and I haven't found a reasonable company (eg., one that gets good reviews) that seems to offer the service I need. If I should be working directly with an airline, anyone have suggestions about which one to use?