go to the header template (located at your_package/yourtheme/template/page/html/header.phtml)

move the part

<div class="quick-access-container">...</div>

to the top of the code: 

<div class="header-top">...</div>

go to the header template (located at your_package/yourtheme/template/page/html/header.phtml)

move the part

<div class="quick-access-container">...</div>

to the top of the code:

<div class="header-top">...</div>

go to the header template (located at your_package/yourtheme/template/page/html/header.phtml)

move the part ... to the top of the code: ...

go to the header template (located at your_package/yourtheme/template/page/html/header.phtml)

move the part

<div class="quick-access-container">...</div>

to the top of the code: 

<div class="header-top">...</div>