I fixed a crack in my rudder by 'glassing both sides of it. I used thin epoxy resin and squirted epoxy into the crack before glassing the sides. My crack ran from one of the bolt holes to the back of the rudder (probably only 2 or 3 inches long). The glass adds strength and helps hold the opposing sides of the crack together.
Glassing means you are glueing fiberglass cloth to the wood. You'd roll some epoxy on the wood, then lay a piece of fiberglass cloth in the wet epoxy, and then roll more epoxy onto the glass, filling the weave. When the epoxy cures the fiberglass cloth is bonded to the wood.
I was familiar with the process from cedar strip boat building. If you don't have access to some fiberglass or someone who's done this kind of thing, it's still certainly worth a try to just use epoxy and really get it into that crack. The wood around it would probably break before the epoxy joint did.
For such a small job, if I didn't already have epoxy on hand I'd probably just go and get one of those double tubes of epoxy and hardener you see in hardware stores, Wal-marts, Menards, etc.
They look like two syringes stuck together side-by-side.
You just cut the tips off and press the plungers and equal amounts of epoxy resin and hardener come out. You mix them together well and apply.
Just make sure it says waterproof on the package, and get one with a cure time of at least 30 minutes. Longer, if available. Some of them cure in 5 minutes and you'll want more time than that to work with it. It won't be easy to get it in a small crack. This stuff usually isn't thin enough to squirt through a syringe. You'd probably need to slightly spread the crack and then try to force the epoxy into the crack with a putty knife.
There are many brands and I'm sure some are better than others.
The epoxy I have on hand from boat building is from U.S. Composites. Trouble is, the smallest amount you can get is a 24 oz. kit (16 oz of resin and 8 oz of slow hardener) and costs $15.50, plus shipping. See it at http://www.uscomposites.com/epoxy.html
The nice thing about this stuff is you can suck it up in a syringe (minus the needle) and squirt it into the crack. You can get syringes from stores that cater to large animal owners. I haven't found any that had a big enough needle for epoxy to pass through, but there could be some out there.
You can also buy fiberglass cloth from these folks. The epoxy I note above would be perfect for wetting out the cloth. The fiberglass cloth method is a much stronger way to do the repair.
For big gaps or glueing 2 pieces together, you'd thicken the epoxy with sawdust to a peanut butter consistency. For that kind of work you might want to consider the fast hardener.