My first instinct would be to check QTC (part of the Designatronics group familiar to many via their SDP/SI division). Although I realize it’s not the ratio you were depicting above, you should probably look at this page, specifically SBS1-4020R and SBS1-2040L to get an idea of what’s available, and what it might cost you. Those teeth are induction hardened to Rockwell C 48, which in steel, correlates well with a tensile strength of about 1 632 MPa (237 000 lb/in2, or really strong). The teeth are 1.0 module (or 25.4 diametral pitch), which I’d say is about as small as you’d want to go for a final stage of a drivetrain—and even then, only with a hardened gear.
And by the way, if you need more clearance for the pinion (too wide), you might consider dishing out the wheels facing the centre of the gearbox (so that the pinion and gear sit in a depression in the wheel, sort of like a typical west-coast style wheel with the spokes on one face).
Typically, in FRC applications, gears fail because the teeth are overstressed. (Other failure modes are possible.) The important characteristic is therefore the bending strength of the teeth.
There are a few ways of evaluating this, with varying levels of complexity and accuracy. The Lewis-Barth method is traditional and conservative, and requires relatively few parameters. AGMA has another method that takes fatigue and contact stress (another failure mode) into account, as well as a whole slew of other design factors—but you probably won’t know what values to assign to them without some sort of basis for comparison. Given that bevel gears are a bit of an unusual system for an FRC application, I’d avoid relying on rules of thumb alone (so don’t just take my word for it).
For an introductory reference, see this. Check out the literature provided by the manufacturer. Also, there’s this: a whole book about gears, with a good explanation of the Lewis method. For more about the AGMA method, I recall that any recent edition of Shigley’s Mechanical Engineering Design should include a chapter (written for upper-year mechanical engineering students). You might find this a convenient resource for equations and examples. Definitely search the Chief Delphi forums for other resources.