Not really, cos after I got here I was reading on the intranet of my company that they arrange import permits for QR10! Of course you would have to do to customs bit yourself once the cat is here, but you would have to do that anyway if you'd be bringing your pet as accompanied luggage. Contact Qatar Airways (or whatever airline you'll be using) and ask them if you can do the export yourself. It can save you lots of money!
Also contact your company (or your hubby's), they are likely to handle the import permit for you.