1. Get the Developer Facebook app. Type "Developer" into the Facebook search bar and click on the first result. Click "Allow." Now you're a developer.
2. In the top righthand corner of the Developer app, click on the "+ Create New App" button. Fill out the App display name and description. (Just make something up or type gibberish; this won't actually create an app that will be visible).
3. Agree to the Developer privacy agreement. TechCrunch says you need to have a "verified account" for this, which means that you'd need to have a credit card attached to your Facebook profile; I don't have a verified account, however, and I was able to get the new profile.
4. Find the "Open Graph" on the left sidebar and type in a test verb and noun for your new app. I started a "Bake a Cake" app, so my test verb will be "Bake" and my test noun will be "Cake":
5. Run through a few pages of new app information. No need to enter anything here, just keep on saving changes and continuing.
6. In five to ten minutes, you'll have an invitation at the top of your Facebook profile to try out the new profile. WARNING: It might be buggy.
[UPDATE: If you decide afterward that you don't want the new timeline for any reason, it's very easy to revert back. Go back into your "Developer" page and click "Edit App." This will bring up a sidebar on the left side of your page. Click "Delete App." After you do this, your profile should be reverted back to the original.]
This is option one and is obviously not for everyone. Option two is to sign up for beta notification right here. When Facebook is ready for users to test out the new profile, you will be emailed and get to try out before all of your friends.
And voila! Those are two ways that you can get the new Facebook profile immediately, if you're desperate for the change.