Got this info from a friend in Guernsey:
I think you can fly over with Blue Islands
http://www.blueislands.com they
aren't very cheap though or alternatively you can catch the Fast Ferry
www.condorferries.co.uk from either Poole or Weymouth. You do not need any
innoculations/treatments to come to the Channel Islands it is the same as if
you were travelling around the UK.
If coming over on the Fast Ferry the dog would be in the car on the car
deck. Members of the cabin staff will come down and check the dog for you
though but I've found that they are very settled and go to sleep for the
whole journey. It is usually us humans the suffer on the boats with sea
sickness.
If coming over with Blue Islands on the plane the dog can usually sit next
to you but you will have to pay extra for this and they ask that you put a
muzzle on them and bring a blanket. I've done this from Guernsey to Jersey
which only takes 15 mins and have put a halti collar on the dog rather than
a muzzle.