Hi DorisP, I love carrot cake, it is one of my favourites. I wondered if you mixed your icing sugar first with some egg white, let it stiffen up and then mix with the cream cheese, that might make a much firmer icing.
I have also found this recipe for cream cheese frosting in one of my cookery books. 30g butter softened, 80g cream cheese softened, and 240g of icing sugar. You beat the butter and cream cheese until light and fluffy and then gradually beat in the icing sugar. This sounds like quite a firm frosting as the butter will harden a little when it is set. Hope it works out.

busy_lizzie