Janet at Qatar Pet Relocators has been very helpful in handling things when we brought our cat over a couple of weeks ago: www.qatarpetrelocators.com
Our vet was also an invaluable source of information on what paperwork/injections/expected timelines, especially chasing DEFRA for the export licence. If you're in the UK, this may help: https://www.gov.uk/take-pet-abroad
Good luck - we found it more challenging to get our cat sorted than ourselves!