Baking – How to organize making a cake days ahead

Generally, no they should be fine. You'd have more of an issue with frozen than fresh. It would take fresh strawberries a long time to release enough moisture to cause any significant amount of sogginess.

The issue you're more likely to run into depending on the size of your strawberries, the density of your Bavarian cream, levelness of your cake, and the weight of your top layer is that they can act like rollers and friction between the two layers will be low. If the cake is tilted wrong, the top layer will just slide right off. I've definitely had it happen - ruined a cake for a charity event :(. Make sure the strawberries are cut into bits - not halves or slices and preferably fold them into the cream to prevent this from happening. All the flavors will still be there, but your cake will be safer.

Are you sure you want to use icing? The barbie cakes I have seen all have the skirt made from rolled marzipan, not from icing. The bodice can be a normal fabric top or dress (inedible, can be washed after the cake is eaten) or also molded from marzipan. I agree that it isn't as tasty as buttercream icing, but it surely makes a more beautiful skirt.

This recipe has 196 pictures, you can see different variations of the bodice.

If you insist on using icing, I would try to smear something sticky onto the doll first, for example honey or syrup in the softball stage, then apply the icing on the sticky layer. I haven't tried this myself (nor have I tried applying icing directly to plastic, so I don't know if it will hold).

On another note, don't forget to put the barbie's legs in a cut-off paper towel cylinder, so she doesn't get damaged when the cake is cut, and doesn't fall when pieces of the skirt are missing. Also, if you bake the layers in a guggelhupf pan, you don't have to cut a piece out of the middle, which is hard to get right.