I am fairly new in this business and today I had an order for a sheet cake and she wants the baby carriage design from the napkin on top of the cake. What would be the best way to do this? Royal icing transfer??? She needs the cake on Friday.

You could copy the picture (mirror image), trace the pic with piping gel, flip onto the top of your sheet cake and fill in with either stars or go over lines with royal icing and fill in with color flow.
OR
Copy and cut out the pic to use as a template, piece by piece, and cut out pieces in fondant and patch them together on top of the cake.

Any of the above or you could do:

1)FBCT
2)Chocolate Transfer
3)Pinprick method
4)RI stamp
5)Edible Image
6) and of course free hand (mind you if I did that no one would be able to tell it was supposed to be a carriage ).

Go to a copier and enlarge the photo on the napkin so its the same size as you are going to put on the cake (even if it takes two sheets of paper). Copy it from there using any of the above methods.