Modify menu position in child theme

Hello,
I am new in wordpress and I am already building my first site. I have been reading about wordpress and how to properly work with it but I have a few questions which I expect you guys to answer me.

I am using a child template to avoid make modifications in the core template, which is twenty thirteen by the way, now I want to change the position of the menu, what should I do? Copy the header.php file inside my child template folder and then modify it? And if I do this and the parent template updates, my new header.php will updated too? It is the correct approach?

Thanks in advance