Is there a way to set Height to a Drawer Header?

You wrap this with a SizedBox widget.

const SizedBox(
   height: 64.0,
   child: DrawerHeader(
       child: Text('Categories', style: TextStyle(color: Colors.white)),
       decoration: BoxDecoration(color: Colors.black),
       margin: EdgeInsets.all(0.0),
       padding: EdgeInsets.all(0.0),
    ),
);

You can use SizedBox widget for resize height DrawerHeader

new SizedBox(
   height : 120.0, 
   child  : new DrawerHeader(
      child  : new Text('Categories', style: TextStyle(color: Colors.white)),
      decoration: new BoxDecoration(color: Colors.black),
      margin : EdgeInsets.zero,
      padding: EdgeInsets.zero
   ),
);