Does anyone have any tips on how to bake and make a pacifier cake?  Something like this?? What would the part that sits on the lips be made of?? 

I think for something that size, I would cut the shape out of a cake card and covering it in fondant - the picture looks thick enough to be done this way. I'm not sure I'd trust a piece of gumpaste or CMC-strengthened fondant to hold up without an internal support.

wow that is look good

Does anyone have any tips on how I should bake it? 

I would bake a circle for the handle..  And a sphere for the pacifier.  I would then connect my cut out centre of the circle  to the base of the sphere to extend it out.  I made a swimming tube for a minion cake that way (there's a pic in my photos).   I left the dome along the edges of the circle to keep the rounded shape.

That's a cool idea for a baby shower cake.  I've not come across one like that before.  Good luck with yours!  Looking forward to pictures.

Here is the cake. I baked a Dolly Varden cake for the actual pacifier and carved it and then carved a round cake for the handle. I used cardboard for the middle. Thanks for all the help and tips.