hi antiquepedaler,
There have been a few posts on the topic as far as a corral for carrying dogs. Someone wanted to build out the rear well like a wagon to keep the dogs from jumping out. If they are well trained and not panicky they should be fine just sitting in the well. I personally am not big on a pet inside a hatch in the event of a rollover you could have a trapped pet.
I have a 95# labrador retriever and thankfully she is well trained and will not jump overboard but she does get over excited and jump around in the well. I use a carpeted/rubber backed floor mat in the well so she has traction. The slick plastic can freak them out not having traction.
A typical mat at Home Depot for $10.00:
http://www.homedepot.com/webapp/wcs/sto ... 0003+90401
Staying close to shore the first few times till they are used to the kayak is recommended. Remember this .. it will become their NEW WALK and you will not be able to go out alone without them getting upset.
They will go nuts every time they see the paddle as they do when they see a leash.
I have only taken her out when I have the Sidekick Amas (outriggers) installed on my revolution as a safety precaution against rolling over. She loves riding in the Kayak. The Sidekick also gives stability to bring her back in the yak just in case she goes over.
Often she just lays down and enjoys the ride until something like another dog ashore or on another boat excites her.
It is always nice to have your best friend along with you and treat him/her as one of the family and make your pet wear a PFD. The handle makes for easier retrieval.