Do you put the board that you iced your cake on, on the fondant covered cake board? You don't try to get the cake off the board to put on the covered cake board, do you?
Cover your base with fondant, and allow it to dry. Then set the first layer of the cake in the spot you want it. Don't remove the cake board. The cake board helps maintain the freshness of the cake and dried fondant would want to absorb some of that moisture.