Is my pegboard stand design reasonable?
You'll need a good rigid frame. I don't think 1x4 will do it, pegboard is very floppy.  I'd probably suggest 2x4, and use two sheets of pegboard to conceal them some, sandwiching the 2x4s between two sheets.  The other advantage is that you won't see the hooks from the opposing side.  One complication is that it's likely to be top heavy so you need to make the base "outriggers" quite long so it doesn't fall over.

It will be pretty simple other than the angled cuts, which you can figure out empirically by laying out the inverted T portion of the base, and then cutting the braces to fit.  There are many good introductory books and websites, take a look at Taunton Press, I'm sure they have plenty. When you buy your lumber get "KD" 2x4s rather than run of the mill stuff which will have high water content and tend to warp as it dries. The stuff you want will feel relatively light for it's size.  Sight down each edge and look for twists or warps.

OK, that get you off to a good start?