Hi. It's not posible to move elements from one place to another in predefined Headers. You should create your custom Header and Top Bar. Then you can plase things where you want.

Turn OFF predefined Header, go to the Layout tab and create two sections called Header and Top Bar with number of columns and module positions you want.

Or create your own predefined Header via coppying of one of existing in the same folder. Rename it and change its code.

All these things can be found in the Helix documentation