You certainly can take everything you need, by suitcase or shipping, and make the cake there. I did a baby shower cake last October. I flew from SC to Chicago with two suitcases, one carry on suitcase, and had ordered some things on line and had it shipped to one of my sister's house. I didn't bring my mixer because they already had a KA, not as big as mine, but big enough to do it in batches. We made the cakes and frosting there, and I did the cake from beginning to end. My family was astounded at the amount of time it takes to do a completed cake from start to finish. They had no idea of the equipment needed (I brought my big stainless steel rolling pin...lol) and the attention to detail to make it all work.
I set up a box in my cake room and every time I thought about something I would need, molds, etc. I would get it out and put it in the box. I included the cake pans, cake racks, parchment paper, fondant rolling mats, color dusts, gel coloring, brushes, palette knives, you name it I took it. I gave my sister a grocery shopping list for all the ingredients for the cakes (strawberry, chocolate and vanilla cake) and the icing, I ordered sweetex and had it shipped to her house as well. Sent her the dimensions for my cake board and I brought my cake board covering material with me. I purchased some small clear containers to hold my brushes, palette knives, exacto knives, blades, etc. I labeled each container and each one that had knives, etc I labeled with "caution...sharp cutting instruments enclosed".
My biggest challenge was the actually crib pieces: two end pieces and two side pieces that were very large and made from gumpaste fondant mix. They ended up being about 1/3" thick and the cake was a 12" x 18" three layer cake. I made carrying cases for the crib pieces out of foam core and placed each crib piece after it dried between two layers and taped it shut all the way around. I wrote on each one what it contained (for airport security reasons). I used a scrapbook paper carrier and made trays out of foam core with individual compartments for each individual pre-made decorations (26 teddy bears, each holding a letter of the alphabet). I also used some 1" thick foam to cushion the bottom and top trays in the carrier. Everything made it all in one piece and nothing was broken!
I am glad that I had the opportunity to do this as it showed me what I can do away from home. The key to all of this is planning, planning, planning:). If you have any questions, please feel free to PM me!
Good luck, and don't forget to post pictures:)