What motor are you planning to connect to it?
What gear (1st, 2nd, or 3rd) do you plan to use?
Depending on your expected output torques it
might be impossible to have adequate strength without heat-treatment.
I would consider 6-4 Titanium, 4130, 8620, or 4340 steel.
"But Titanium is so expensive!" -- It's lighter, stronger, and IMHO very appropriate for this application. And you could get a 0.500"ODx36"L titanium bar from
http://titaniumjoe.com/6al-4v%20round%20bars.htm for ~$60, from which you'll be able to make many output shafts. It will be a little more difficult to machine, but still very doable.
4130/8620/4340 are fairly inexpensive, not terribly difficult to machine well (get some carbide insert lathe tools though) and has good strength (8620 is the strongest). They can also be welded very easily (ER70S-2 TIG wire is good for these low-carbon alloys) so you could weld on an output gear or sprocket without much difficulty.