the wooden dowel through the foam is an often optional step that sometimes gives a piece some extra rigidity. More often than not, it is just a mechanism to attach a sword-hilt to a foam blade in such a way that it won't come loose.
Usually the way it is done is by carving a half-cylinder into two pieces of foam and sandwiching them together with the dowel (or PVC pipe) inside. Some people bore a hole with some sort of auger.
I only use a few dots of polyurethane glue (e.g. gorilla glue) to sandwich foam together. I use it more liberally when embedding a rod. PU glue expands into a foam just a little bit as it cures which fills the voids of the foam caused by carving a half-assed cavity.
The reason I just use a few dots is because when using a composite technique, that glue isn't really what holds the foam together. The pieces are held together by the rigid shell of paper-mache or fabric+glue or fiberglass+resin. This is also why reinforcement doesn't need to go all the way through the core of the foam.
Putting this together in a sturdy manner might be a bit tricky. If I did it, the handle would be a PVC pipe. For reinforcement on the blade, I'd use a 1/4'' piece of brass tube something like 6-10'' long. I'd drill a 1/4'' through each side of the pipe and work the brass rod through so about 1/3 is sticking out one end, 2/3 out the other. I'd then bend the rod into a rough curve, as needed. When happy, epoxy or superglue the rod in place on the pipe. I'd then carve a quarter-cylinder along the edge of each rough-cut piece of foam matching the diameter of the pipe such that the foam can be butted up tight against the handle. I'd press the pipe into each slice of foam for the blade (One slice above the rod, one slice below it press together just enough to make a dent along the length of the rod) and scoop out the indentation it makes until the rod fits. Then sandwich the two pieces together and glue. Then carve out the blade, and harden it with paper mache or whatever, wrapping the reinforcing fiber of choice around the pipe as well as the foam (not the whole pipe, just at that joint). Once dry, I'd sculpt both the skull and the shorter end of the blade out of epoxy clay. The clay for the shorter end of the blade, naturally, will be wrapped around the shorter end of brass tube sticking out the pipe. Then do whatever filling, additional sculpted details, sand, prime, paint.
But, that's just me.