I have been chosen to bake the birthday cake for my boss, no big deal except she wants carrot cake and I will be using a boxed cake, but normally when I do a box cake I add pudding to make it more moist. What kind of pudding should I use or should I not use pudding?

I would use vanilla.Or unflavored.

AVanilla or white chocolate

I use boxed mixes with pudding added a lot, but for a carrot cake, I'd be inclined to make it from scratch.  They're generally so moist (and delicious) with the fresh grated carrots.