If you are planning airline travel for your kitty within the United States, or travel by any means to another country, your cat will need a health certificate. Issuance of health certificates is regulated by state and federal government, and laws regarding import of animals are a matter for the country you are importing to. Veterinarians may only issue health certificates if they are federally accredited (I am and have been since 1983). Airlines typically require health certificates even if the animal is flying within a single state.
In order for us to issue either an interstate or international health certificate, we will need to examine your cat during an office visit, and you will need to make an appointment for this. WE CANNOT LEGALLY ISSUE A HEALTH CERTIFICATE WITHOUT PERFORMING A PHYSICAL EXAM AT THE TIME IT IS ISSUED. This point is not negotiable. Advance planning is the order of the day - you should look into legal requirements as soon as you know you are traveling - please do not wait until the day before you plan to fly to Australia or Hawaii to start the ball rolling.
Call your airline or check their website to find out what their travel requirements for pets are. How much does it cost to fly your pet? What restrictions are there on pets traveling in the cabin (carrier size is an issue here)? What sort of paperwork is required for your pet to fly (airlines differ greatly here - some no longer require health certificates at all - some are very strict in their requirement that you provide one).
Do your due diligence and check your state websites, too! Hawaii is the only state with major restrictions on animal importation due to its rabies-free status. The four-month process with allows you to import a cat to Hawaii without a lengthy quarantine is not often fully complied with, so some owners, after doing what they think is the right thing, STILL wind up having to quarantine Fluffy for 4 months at the end. Don't let this happen to you - it's a horribly expensive mistake and very distressing for pet and owner.
This is where we see lots of problems leading up to transport. Failure to adequately plan for transportation and allow enough time to comply with all regulations imposed by the importing country is a constant and ongoing issue. Fortunately, due to the wonders of the internet, owners are much better able these days to navigate the minefield that shipping a cat to someplace like Japan or Australia or England can be. Every country has a website that spells out the process in plain English.
Most countries don't require anything other than an exam, health certificate, and current vaccinations (particularly rabies). In these cases it's a simple process involving only one vet visit, generally within a week or two of travel. If you need to submit the health certificate to the USDA in Sacramento for their stamp of approval, you need to allow time for that, too.
If you are traveling to a rabies-free country, be prepared for a long, drawn-out process of exams, vaccinations, blood tests, microchipping, more exams, more vaccinations, etc. And you have to get it JUST RIGHT, or it's the same as not complying at all. So again, do your due diligence and know exactly what you are getting into. Never take a cat to a foreign country on a whim or if it's not absolutely necessary.
Here are links to the pet importation web pages of some of the most common (or challenging) travel destinations:
Hawaii pet importation brochure - this thing's more like a book!
Hawaii Department of Agriculture
Bringing Cats and Dogs to Australia
Traveling With Pets to the UK
Taking Pets to Japan - translation is a little bit problematic with this website, in my opinion. PDF of current requirements is HERE.
And here's the USDA page on pet travel with important links.