Hickory backing from 3 rivers will cost more than a board merits. I'd consider a simple cloth backing. Or perhaps having the cabinet maker rip a maple, pecan (basically hickory), or even from another red oak board. I'd also consider adding a 12" section to build up the handle and fades in the center, 1x2 is fine.
But honestly, I've made my fair share of what I'd call good bows, none from red oak boards both backed and unbacked. I think it's great as a learning tool, but would not invest a great deal of money, when "better" alternatives are at hand, if you are gonna spend money. A hickory stave off of ebay, classified ads, or 3 rivers for that matter, for example.