I'm actually working on something similar for my friend's wedding shower. I'm making my cake stand up with a wooden dowl about 3/4" wide and I'm going to attach that to a cake board at the top for the cake to sit on and screw it into a platform on the bottom to be the base. I'm still trying to figure out how to make the umbrella shape for the cake, so i baked a cake in a large pyrex bowl (about half way filled with batter) and then i'm going to use a 10in round cake for the bottom layer and kind of taper the bottom layer to fit better with the top. I plan on covering it in buttercream and piping the lines that would be the spine down the sides. I think covering the cake board in fondant would be best, that way it wouldn't sick out so much and the cake would look like an actual umbrella standing up. To help cover the base I'm going to dye a little bit of cocount to make it look like grass, or you could even use Easter grass which is out everywhere now. Email me and let me know how you make out, maybe we could help eachother along (email@example.com). My shower is in May so I've got a little bit of time to work with. Right now I'm just trying out my ideas but my cake came out with a decent dome shape. You could also use fondant to make the scalloped edges at the bottom to make it look more like an umbrella. Another option would be to bake a 12" round cake, cut it in half so you have a semi-circle, and put one layer on top of the other and decorate. Still use the wooden dowel for the handle, just wrap in ribbon, or cover in fondant to give it color.