Trust me - I am an expert in carrying police dogs - ask anyone who knows me
Dogs should be treated as loose cargo and should be housed in cages designed for carrying dogs. They are loose unknown quantities and IF they kick off in flight you are seriously embarrassed.
They can easily be trained to embark/disembark into the dog cage without any fuss and they love it.
Details on the cage can be obtained from the EC135 fraternity in the UK.