Welcome to Dreamhost!
Yes, generally speaking. Depending upon the software you are running. you may also need to use other directories (folders), but the directory labeled with your domain name is your "main" web accessible directory.
It's a little confusing how to interpret the message, not knowing how you "uploaded" Drupal. Did you "install" Drupal, or just move your files from your old host? The answer to that question, and what, if any, changes you made to your settings.php file to facilitate the moving of Drupal between the hosts has a bearing on how to interpret the error. All this assumes that you already created your Dreamhost-based MySQL database to hold the Drupal installation via the Goodies--Manage MySQL screens of the Control Panel; I assume you did that, as you mentioned using phpMyAdmin (and assuming you are using phpMyAdmin on Dreamhost not on GoDaddy).
Dreamhost uses multiple versions of MySQL, depending upon which MySQL server your database is set up. You can tell which version of MySQL you are running by looking at the top of the "left hand" column of the "main content" frame of phpMyAdmin; the Column Title is the MySQL version. Not knowing what your Drupal settings are, or what version of MySQL you are running, or how your 4.2 database was "exported" from your GoDaddy installation, I can't be sure if that error message actually means you have a version mismatch, or whether it is a "general" error message that could be indicating you have problems in your settings.php file. At the very least, you would have to change your host, user, and password (and possibly your database name) in that file after the move to be able to connect to the database.
If you are able to reach your domain on Dreamhost using your domain name, and you can access your DH database via phpMyAdmin, I don't see any way the GoDaddy nameserver changes could be relevant. It is more likely that one or more "steps" involved in moving Drupal have not been successfully completed.
Make sure you have reviewed the Dreamhost wiki article on Drupal", as there is considerable information there that, while tailored for "installing" rather than "moving" may be helpful. You might also want to explore a bit on the Drupal support forums for "moving" a Drupal installation - for instance, here is a thread for the Drupal Forum on moving an existing Drupal site to Dreamhost, that seems to have addressed several difficulties and provides additional links (there are probably others as well; I just included this one as an example).
After checking out those links, and/or if you have any further questions or need additional help. there are several people here that run Drupal who can probably help. Good Luck!