Hmm, I don’t think so. Oftentimes, I halve a recipe that calls for that size pan into an 8" or 9" square baking dish. So I think you should be OK. If anything, maybe check around for cooking times for a smaller recipe in a 9" pan or keep it simple and maybe check 5 minutes sooner than the baking time for the original recipe. I’m thinking of even a Duncan Hines box mix, it would provide different baking times for 2 smaller round cakes vs. 1 9 x 13". Happy baking!
ETA: Just for example, here’s an apple cake in a 9" pan you might use as a comparison for ingredients and baking times. Hope it helps.
