Professionals ice on a turntable. Turntables for home use are affordable, and make icing much easier.
Your spatula should reach to about the centre of the cake when held steady and comfortable. As @rfusca suggests, heating it for buttercream is a good idea. You can also wet it for other icings, to make it glide smoothly.
For the icing process itself, start with the top of the cake. Apply a generous amount of icing; you will be thinning it out with the spatula, not smearing it right and left to get an even thickness. Hold the spatula to an angle to the cake, tip at the centre, and rotate the turntable. Let excess icing drop to the side of the cake. When you have done the top, smear icing thick on the side, hold the spatula vertically, the edge at 45° to the cake side surface, and again turn the turntable. When you have finished, you will have raised icing on the edge of the cake. To finish the cake, smooth these edges.
To do this, you need enough icing. "The professional chef" recommends 340 g (12 oz) for a 20 cm (8 in) cake and 454 g (1 lb) for a 25 cm (10 in) cake.
This all assumes buttercream icing or other spreadable icings such as ones based on whipped cream or creme fraiche. It is somewhat tougher for semi-liquid glazes such as ganache.
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.
Best Answer
There are a few things to look at here:
It looks like your original question has more to do with the cake itself before icing. Good quality cake pans are the key to getting a cake that is a consistent shape, and to make sure you put enough batter in the pans to get the size and shape you want. Make sure you have straight sided pans that bake your cake evenly.
http://www.amazon.com/Wilton-Aluminum-Performance-9-Inch-Round/dp/B00006G958/ref=sr_1_12?s=kitchen&ie=UTF8&qid=1396099879&sr=1-12
This link is to an example of the kind of pans that have straight sides. I have three inch deep pans, rather than two inch like the ones in the link.
I would avoid cutting a cake down to size, as you will likely have crumbs everywhere!
On to the icing parts: