Unless you are determined to use the paddle to build up your muscles for paddling, I would not suggest jarrah for a paddle.
Check the density of jarrah. I found a site recently with the exact figures and of course I have now forgotten where it was.
Take my word for it, jarrah is heavy.
While I have not made a greenland style kayak paddle, I have made a few canoe paddles using alternating 3mm strips of balsa and western red cedar for the handles. The strength comes from fibreglass or carbon fibre tape sandwiched between the outer few layers. In spite of being much lighter than commercial recreational paddles and almost as light as the better competition paddles, I haven't broken one yet.
If you are making a strip built kayak, the strength comes from the glass skin, so why not accept the same principle and use the lightest timber possible with a glass skin providing the strength.
I would suggest western red cedar. Laminate the timber to avoid wasting timber by buying unnecessarily large planks.

Allan Newhouse
Bowning
Australia