i dont think you can just bring your pet to another country that easy. unless you're rich.
but i had to let my parrot in Mexico when we moved to Canada
edit:could just be a story from my parents and not a real border problem)
My wife got the job in Australia. Paid her big money in AUD when the AUD was worth more than the USD, and they ponied up for relocation.
Process for a dog is 6 months. You take a rabies test, and that's when the clock starts. The way it worked then was the process included a minimum of 30 days quarantine, so we waited in the US for 5 months (which was fine, because I stayed to sell the house and finish up business), then our pup spent the last 30 days of the 6 month process in quarantine (it's now been lowered to 10 days quarantine).
The whole cost, including the move, paying a service to make sure the paperwork wasn't screwed up, and quarantine housing was about $8000, and there were a couple of hiccups along the way.
First, my vet sent the rabies test with an extra 0 added to my dog's microchip number, so it didn't match. We got the government to accept the results provided we took a second test, with the correct number, and it didn't vary from the initial result.
Second, my dog dropped about 10 pounds in a week and a half. I handed her over on a Monday for holding before the flight. She flew Wednesday. I'm assuming she didn't eat then. She arrived Friday morning Australia time, and didn't eat until Sunday morning, when one worker rubbed her belly while another hand fed her. By mid week, she was eating semi regularly and then was fine a few days later, but over that period, she dropped from about 52 pounds to 42 pounds.
Third, I was allowed to see her the Tuesday after she arrived. My wife and I drove out to the facility from just north of the city. She wasn't happy that we didn't take her then. Anyway, after that, I'd go to visit . . . I'd walk 2 kilometers to take a half hour ferry to catch a 45 minute train to a place a 20 minute cab ride from the quarantine facility. Each time I visited got shorter, because she'd be like 'you're not taking me, fine, get the **** out'.
Long story short, it was one hell of a process . . .