We are also in the states at the moment. We got our fingerprints done at the local sheriff's office and sent the physical prints along with the printed offline form to Canberra. We got a link to download our approved certificate about 2 weeks after they received our documents.
As a side note, Fedex, UPS and DHL don't directly deliver to the locked bag address provided on the form. We used DHL and received tracking to Canberra, but a third party completes the delivery so you won't actually get confirmation it has made it all the way. I emailed for an alternate address in case it had to be diverted, and they suggested;
AFP Criminal Records
Level 1, 53-73 Alinga St
Canberra City ACT 2600
You should get tracking the whole way with that address, but ours made it to the locked bag eventually so maybe not necessary.
Good luck, postage from the US isn't cheap!!