I took my 9 year old son out in a Slayer Propel 13. He weighs about as much as your dog and he was able to sit in the front hatch (no, I didn't bungee him down
). The kayak was definitely front heavy but I was able to do a short ride with no issues. But you need to consider a few things.
I don't weigh much and I didn't have any gear in the back so there wasn't much weight to balance the kayak. Also, I have the seat pushed way forward so that's even more weight to the front.
The further forward you have the seat, the more room you'll have behind the chair for tackle. The rear compartment (not the area directly behind the seat) is about 24" long and the dog would probably have plenty of room there.
I wouldn't consider the area directly in front of the chair to be a possibility.