You can try the free demo version of EZNEC: www.eznec.com
A quick model suggests around 7uH should be a good starting point, which, with zero
losses would have an input impedance around 17 ohms.
This coil calculator will help you calculate the physical dimensions:http://hamwaves.com/antennas/inductance.html
With a small diameter coil wound on the fishing rod itself, and depending on your
ground system, you may have enough loss to get a low SWR with no other matching.
If you can keep the loss resistance down to 11 ohms you'd have a 2 : 1 SWR, which
could be matched using a shunt coil across the feedpoint - the exact details will depend
on the Q of your coil and the details of your radial system.