I'm sure I've read that pointing more than one URL at a site can damage it's ranking abilities? unless you use a 301 permanent redirect as google recommends.
I know that google doesn't like redirects, so I'd be concerned about doing what has been suggested, what would be better is buying hosting with your new URL and setting up an informative site of at least a few pages filled with plenty of applicable content and provide links to your original site from there, if your new site can gain plenty of links and google pagerank it should help the original site.
I actually tried directing another URL at an existing site and the original site never got any pagerank for months until a few days after I stopped the redirect! could have been coincidence?