In a nutshell, I'd have to say don't even try. it's almost certainly going to be such a pain in the ass that you'll wish you'd either stayed home, or left Fido at the pet-sitter's, or both. Many (not all, and it may (don't know for sure) be that you can get a waiver in some cases) countries have an "absolutely no deviations allowed, ever, for any reason, period! Shut up, the discussion is over!" level mandatory quarantine period for the critter, which might be anywhere from 7 to 90 days, depending on the county you're entering. The costs, including governmental markup, taxes, fees, and surcharges of this quarantine fall on you, and can get into 5 or 6 figures to the left of the decimal point. Some countries are worse than others, some better. Iceland being a prime example - they have one of the strictest (if not THE most restrictive) regulations in the world. Essentially, *NOTHING* *EQUINE* *GETS* *IN* *PERIOD* - as I understand it, if you attempt to bring a horse/mule/donkey/zebra/quagga, or any other equine into iceland, you have two options: (A) It never leaves the boat until the boat makes landfall somewhere else, or (B) it gets shot (or chemical equivalent) and the carcass is immediately delivered directly to the nearest incinerator big enough to fit it through the loading hatch - take your pick. They're *INCREDIBLY protective of the Icelandic horse bloodlines, and prevention of any possible equine disease - So much that I understand that if a horse leaves Iceland as an export, it can never, EVER return. It's possible to import stallion semen, and/or ova for AI, but bringing in an actual live horse is absolutely forbidden. Similarly, try to get a cat into Australia, either openly, or smuggled. According to info (true, false, or otherwise? You decide - I'm just passing along what I've heard/read) accumulated over the years, such an ATTEMPT - never mind actually getting to the point of letting Kitty's toes touch Australian soil - is good for a mighty long prison sentence (and that doesn't even consider the "this feline is contraband, and will be destroyed" aspect) And as far as dogs, Who was it? Johnny Depp and his old-lady, I think? - just got smacked *HARD* a year or two ago 'cause he didn't put a couple of those high-fashion, zero-value yap-dogs through the properly approved Australian quarantine/inspection/customs/etc bullshit - flying them in on his private plane, then out again after a stay of I-forget-how-long-it-was for some function or other. Seems to me I recall the fine totaling out to somewhere in the quarter million dollar range.
To know for sure how much headache it's going to be to get Fido, Fluffy, Francis, or other four-legger into some foreign country, you're going to have to do a country-by-country survey of the applicable laws. Anything else is guesswork. Assume that there's gonna be a bunch of paperwork (and probably fees), at least, and probably a quarantine period (and more of a wallet-drain) and you won't be disappointed. You might actually end up pleasantly surprised when it turns out that some little nothing of a country you want to visit has few or no restrictions, but expect that case to be right on the verge of nonexistent.
