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Someone at the Austin History Center might be able to point you in the right direction. I would imagine if anyone has Austin Dispatch archives on microfiche, it's going to be either them or the UT library.
Looks like an authentic signature to me. It would have been typed by a secretary and FDR might have had little or no involvement in the content. As something signed by FDR while president, and on presidential stationery, and to a government official, it will have some value. But the content isn't very interesting, unless the editorial he is commenting upon is especially shocking. You could also contact the FDR presidential library.
You'll want to take care of the letter. The thing most people do when they find something like this is show it to everybody, and everybody touches it and fiddles with it and folds and unfolds it and tears it and the condition quickly deteriorates. That's old paper and therefore fragile. Go to gaylord.com and get something like this: http://www.gaylord.com/Preservation/Archival-Envelopes%2C-Sleeves-%26-Protectors/Gaylord%26%23174%3B-4-mil-Archival-Polyester-Envelopes-with-Edge-Seal-%2810-Pack%29/p/HYB01694
Put the document and envelope in there, keep it in there, don't take it out. You can show it around to people if you want but keep it in the protective envelope always--you know if some curious person decides to try to take it out, they'll rip it. Store it flat and keep it in a dry dark place when it's not being shown anywhere. You may want to just go to a high-quality framing place and have it framed for display in your home, if you like it a lot. You could add to it a copy of the editorial to make it a more interesting piece, too. You might be able to sell the letter for just a couple hundred dollars, but if you bought it retail and nicely framed it would likely be over $1500. So you might want to just keep it because you might value it to yourself more than the wholesale price it would get at auction or that a rare document place would pay you for it.