Hope you can help me with this:

I would like to start with a “One Page” solution. All other pages should have the regular header and menu.
My idea is a CSS code for my page like this:

.page-id-2 #header {
display: none;
}

It works but the header section is still there just without logo and navigation.
I would like to get rid of this too.
After than I will build my special header as a content part.

Do you have an idea?
Many thanks