Is it possible to copy an old database, with all existing posts, to a new domain?
Domain and database name would be different from the old ones.

Comments

Yes

This thread (http://drupal.org/node/46389) about moving Drupal might help. It covers different contexts including cases such as yours. I've moved WordPress blogs from one domain to another on different hosts and Drupal sites from a subdomain to root and these processes pretty much follow the basic procedures of backing up, exporting, and loading up your database and files (esp. images), making any changes to configuration or settings files, and changing any hardcoded urls pointing to your old domain or directory paths. The ff links to related Drupal forum threads and handbook pages might also help:
1. http://drupal.org/node/22281
2. http://drupal.org/upgrade/backing-your-site-command-line
3. http://drupal.org/upgrade/backing-up-the-db
4. http://drupal.org/upgrade/backing-your-site-gui

Thanks! I was unfamiliar

Thanks! I was unfamiliar with backing up too, so this is quite useful information.

nobody click here