Jerry -- Your question isn't a stupid one. (I know it's not because I'm having difficulty coming up with a definitive answer.) You didn't say how you were mounting the 1/4" thick 12" square to the backer board. In addition to screws in the waste area, are you also going to be using double-sided tape or hot glue? If so, and assuming all the glue joints are sound, I'd suggest turning at your normal speed for a 12" object. If you're just relying on the screws, I'd turn the speed down to no more than 75% of your normal speed.
Allow me to suggest another approach to cutting the circles: use a scroll saw. Even a 1/16" parting tool leaves a much larger kerf than a bandsaw blade. A scrollsaw blade takes even less wood and, like the lathe, you don't have to cut the board in half.