
Bottom line, for me 8 weeks is too young to be subjecting a puppy to this kind of trauma, even if it is a short flight, comparatively. I had two youngsters flown out of the UK to Canada, at 5 and 7 months. I also flew, with, a puppy from the UK to Geneva, but he was over 4 months which for me, is plenty young enough.
Can't your dad wait a little before bringing this puppy to Cyprus.
Re rabies. Coming from the UK where there is no rabies (yet!) your puppy would only need a Health Certificate in any case. If rabies vaccination is needed, that can be given, and is better too, once he's over there. The puppies I had both in Canada (and same goes for those I took from the UK to Canada with me when we went over there) and the one flown to Geneva didn't have rabies before going.
Rabies vaccination and a delay before coming, would apply to re-entry to the UK, if it was to happen. Again because unlike other EU member states, there is NO rabies in the UK.