Based on my recent experience renting a canoe from the Fort, I don't think there are any rules prohibiting fishing from a kayak.
You say you want to go early. The Bike Barn does not open until 9, and it may open later in October, so you won't be able to go real early.
And, for what it's worth, there really isn't any place that you will be able to go in the kayak that you couldn't reach by fishing from the banks of the canals.
But, if you really want to fish from a kayak at the Fort, I think you can.
TCD