You do know you can use the autotrace function in illustrator to turn any raster image into a vector image? I suggest the fastest way is to find either a raster silhouette of the country (of which there are loads on the net) or failing that start with a non-silhouette and make one using a raster editor like Gimp.

Also check out vector magic on line, which has a better autotrace function than illustrator and which will make illustrator vector files online for you.