Hi Emma,
I have never flown with our cats, but have often seen people in Alicante airport with cats and small dogs in little carriers!
They use a nylon type of "bag" with a mesh end for the animal to see out of, obviously a solid bottom........the bag that is, not the pet!
I assumed they were internal Spanish flights, because of the Pet Passport rules.
But if you can do that from the UK, I would rather have my pet on my lap to reassure it, than worry about it in the hold.
I think it's a great idea!
Hope you get on ok,
regards,