Of course you can. First you need to install a local server. Here are some choices:
After you create your website all you have to do is to transfer it to your new domain name. There are numerous backup plugins that can do the job. Here is an article that cover some of them. Of course you can migrate it yourself. Here is an article from the codex that covers this option.
If you start using WordPress.com you’ll encounter many issues. Don’t misunderstand me WordPress.com is a great service but won’t help you with your specific task.