I have a website. It's liliwilkinson.com (unsurprisingly).
If you read this blog through an RSS reader (which you should), then you don't have to worry about changing anything. If you have thinkingsofalili.blogspot.com bookmarked, then you have two options.
a) do nothing.
b) change your bookmark to http://www.liliwilkinson.com/a/blog.html, where the blog is exactly the same, but looks a bit prettier.