I made this and substituted 1/2 cup applesauce for 1/2 c oil. No other changes; it came out great--even without frosting in a muffin cup. I baked my 12" round longer just to assure the middle cooked through.
Maybe it was my pan or my oven, but I could not get the cakes out of the pan in one piece. The first time, I used Pam as suggested and cooked for 30 minutes. Second go round I used butter and flour and cooked slightly longer. Third time I tried butter and flour again and cooked for 40 minutes. Slightly better luck but still came out in three chunks.
Oh I forgot...I also add 1 cup each of coarsely chopped walnuts and raisins in the cake, and finely chop. an additional 1/2 cup of walnuts to sprinkle on cake after frosting. Adds a nice touch and covers any frosting blemishes. :)
I have the exact same recipe and get requests to make it several times a year. Only change to my recipe is I half the oil substituting the other 1/2 with unsweetened applesauce. A little healthier. I have replaced all oil with applesauce before. It works and it's great but it gives too much of a fruity taste to what is supposed to be carrot cake.
I've made it 3 times this week. I added 1 cup sour cream and left out a little oil. I didn't use the pineapple, but used 1 cup walnuts. This last time I added a 1/2 cup gold rum. It was delish! A bit like carrot rum cake.