Then you should be able to do this with relatively little greif.
There are two main things you will have to do:
1) Move the existing WordPress installation to blog.yourdomain.tld
There are some things you need to consider before you decide how to best accomplish this. For one thing, if you "move" the existing WordPress installation to another location, it will no longer by able to be upgraded via the "one-click" robot at DreamHost (the robot will have lost track of where it is!).
This may or may not be a significant issue for you. It is pretty easy to install and upgrade WordPress "manually" without the "one-click" robot, but only you can decide how important it is for you to retain the "one-click" upgradability. If it is important to keep the "one-click" compatibility of your blog, you will need to install it over again in the new location using the one-click installer.
If your blog is new, and has only a couple of posts that can easily be re-created, you might elect to just "start over", but if you have significant work invested in your blog (or comments you want to save, etc.) then you will need to export your existing WP data and then import it into the "new" version of the blog you have installed via the "one-click" in the new location.
If you do not care about maintaining future "one-click" upgradeability, then you can use the most excellent guide to Moving WordPress available on the WordPress Codex. It is an excellent guide to all things involved in the process, and explains it better and more completely than I can.
Whichever method of "moving" (install a new copy and start over or import old data, or "move" existing installation), your first step will be to use the Control Panel -> Domains -> Manage Domains section of the control panel to "Add A Domain/subdomain" and add the "blog.yourdomain.tld" subdomain to your account, and make sure it is available and working before you proceed.
2) Install the new Joomla! into yourdomain.tld. - once you have completed the migration of your blog to the new location, and it is working properly, you will need to remove the entire contents of your "yourdomain.tld" directory so that it is empty before you can use the one-click installer to install Joomla! into it.
You can do this with your FTP client, or from the shell, in a number of ways. If you are having trouble with your FTP client handling the "hidden" .htaccess files, or if it does not have a convenient recursive delete function that allows you to delete whole directories and their contents at the same time, you can always just rename the directory to something else, and then create a "new" yourdomain.tld directory in the same location (which will then be "empty" - you can always sort out deleting the "renamed" one later when you have a better grasp of your tools or the shell. )
Once you have done that, and have an empty directory for the one-click installer, just use it to install Joomla! to that dir, and you are golden.
When using the one-click installer to install Joomla!, you can either use the same database that you used for the WordPress installation,or create a new one - either way will work as there are no table name conflicts between those applications (they both use table prefixes to keep their tables separate).
That pretty much covers a "shell-free" description of how to go about it, though there are other ways.
Depending upon your expertise and/or comfort level with editing source files, if you don't need to keep the "one-clickedness" of your WP, you can do it even more quickly by renaming directories, editing configuration files, etc. - but the way I have described is the way that is best documented (given the WP material on moving WordPress).