Just did this. (See leaving on a jet plane). I have used The Pet Relocator (Cassandra Lupens) for all of my moves. There's a 6-month wait between rabies titers and import permit application. Once they are in country, there's a 10-day quarantine.
Personally, it's more stressful for me to see my pets on a plane being stressed out. I much prefer to shell out the extra money to make sure my fur children arrive where they need to get to.
My cat and dog were adopted in South Korea, then flown in to Houston, Texas, then driven for 3 days up to NYC, then flown to Soran, Iraq, then back to Houston, Texas and now we are in Canberra, Australia.