Can I create a WordPress site on a domain registered with Google Apps/

I currently use Google Apps and created a web site with Google Sites. I would like to continue my use of Google Apps, but I would like to create a new site with WordPress to live on that Google Apps domain. I am a novice at this and have no idea how to even do anything regarding the ownership of my domain.

If this is possible, is there a way for me to download WordPress and start creating my new site without shutting down my existing domain until I’m ready to put the new WordPress site on it?

Any help is greatly appreciated.