Safety wise you need to think about :
Carrying out a pre flight briefing with the handler,
covering exactly how to load the dog into the aircraft,
and how to unload again after landing,
making sure the dog is under control at all times and cannot get at the pilot
( who won't thank you if they are bitten !),
or controls and parts of the aircraft that should not be interefered with, chewed, scratched etc.
If the dog is one of the more excitable types, a muzzle is recommended.
Also cover procedures in case the dog does manage to break free,
e.g, If airborne - and control cannot be regained - land immediately,
or if on the ground ensure the handler attempts to call the dog back
to a position where it can be seen by the pilot, and does not go running after it, risking injury from tail rotor etc.
Consider shutting down if the dog doesn't come back etc.
Operationally, it is often a good idea to carry out regular familiarisation flights with the dog(s),
especially if the objective is for them to perform a task as soon as they land,
as the excitement / strange airborne environment might have an adverse effect
on the dog if it is their first flight, and they might not perform as well.