You need to check the Pet IMPORT laws. Once in the USA, driving will not be restricted. You need to check the Arizona laws about pet import also.
I just relocated from China to USA with my dog. I hired a pet transport company. They are a worldwide organization. IPATA (International Pet & Animal Transport Association). They handled all the Vet exams, microchip, pet carrier, transport from China thru Hong Kong to airport, assisted with check-in. Timing is critical and scheduling is important.
You need to check with the airline about their pet regulations. Most airlines will not allow pets in cabin on international flights, unless you have a true Service Animal. Pups that young may have restrictions about international flights.
Me and my dog had to process through US Customs & Immigration. I had my documents and a stack of documents for my dog. Thanks to IPATA processing thru was without a hitch and only took about 10 minutes for the dog. I spent more time in queue for immigration and an eternity waiting for my luggage to spit out on the baggage carousel.
I saw my dog's crate unloaded from the plane before I was able to deplane. He was already in Oversize Baggage Claim before I processed thru immigration.
My point to all this is to spend the money to hire PROFESSIONAL people to handle the IMPORT of your pet to USA or anywhere. Get you pet's documents in order, essentially the pet's passport. Confirm with the airline about their pet regulations. Confirm with the airline they have space on the flight before you book your ticket.
Many people mistakenly believe they can stick their pet in a small bag and do a carry-on then stuff the pet under the seat. This doesn't apply to pets on international flights. Only SERVICE dogs are allowed in Cabin on international flights. Even those are facing more restrictions.
Oh, one more item......You will likely need a crate to transport the pet. EXCEED the airlines requirements.