I love carrot cake and honestly -- if you're going to go to the trouble of making a carrot cake, who wants a low-sugar frosting? Like that's going to make any difference, as sweet as the carrot cake is, anyway.
Some cooks like to do a carrot cake in two layer pans, then fill and frost. In my opinion, that's too much work. I prefer using a standard tube pan (preferably a nonstick one with a removable bottom). I turn the cake out on to the bottom of my cake carrier, do a crumb coating with the frosting, let it chill, then frost the rest, just doing the top and sides. I then press chopped pecans into the frosting. It looks great and is not nearly as much work as dealing with a layer cake.