Thanks so much. I did the substitution. Cutting into the cake tonight, I'll let you know how it went.

ChezSuzanne is right. The brown sugar will interact quite nicely with what you've got going. I wouldn't be surprised if, the next time around, you end up substituting on purpose because you're so pleased with the results.

Brown sugar is essentially granulated sugar + molasses, so you can do a substitution. By volume, you can do 1 for 1 sub; by weight I use 6 oz of brown sugar for 1 cup. If your recipe calls for molasses, I'd back out 1 tablespoon of the molasses called for, otherwise I wouldn't worry about it. Molasses should be a nice flavor in with the carrot cake anyway. The only other thing I would mention is that brown sugar is more hydroscopic than granulated sugar, so it will absorb more moisture in the surrounding air. So the cake might get a little softer faster on the countertop than it normally would. But I'd go for it!