Drill rod would be overkill and unecessarily expensive.
Cold rolled steel would be the material of choice here.

Ken.

Ken: I think you may have missed an important feature of the drill rod.
Cold rolled and plated steel has a pretty broad diameter tolerance and
may be very difficult to fit into bearings. The drill rod will be
tighter tolerance but probably .001-.002 oversize. What this fellow
needs is a short piece of C1065 TPG (turned, polished & ground)
available from many metal supply houses. Very stuff, very straight and
right on the correct diameter. Leigh @ MarMachine