Domain Mapping?

My girlfriend has a blog here with wordpress. I’d like to buy her a domain name for christmas but have her still able to function via her wordpress account (since she doesn’t know how to do coding and all of that). Is that possible? And if so, what feature should I purchase? Is this what the domain mapping purchase is for?

Just to reiterate, i’d like to buy a domain name, and when people type in (example.com) into the browser it goes to her current wordpress page. She should be able to keep updating her blog via her wordpress account and all that.

Thanks!