Add Button to Menu

My client would like me to add a "Book Now" button to the top menu that is styled like a button rather than a menu item. I've tried adding it in to the code, but it won't sit to the right of the menu.
Any suggestions? the theme is installed here: http://bsnvet.net.au/ I've removed the button I hard coded because it kept sitting in the center of the menu bar.

Please place your code of button where you want to display the button and i will provide you CSS to style your button in that place. Correctly thanks.

I've added the button: http://bsnvet.net.au/

https://prnt.sc/l7mm9z This is where I'd like the button to go

Go to wp-adin >> appearance >> customize >> additional CSS and add the following CSS. 

.header-wrap .button {
 margin-bottom:0px;
float:right;
}
.nav-wrap nav {
   float:left;
}

That worked, just wondering if it is possible to get it looking more like this:

https://prnt.sc/l8jpzg

Thanks heaps for your amazing support

Remove the code i gave you before by going to wp-admin >> appearance >> customize >> additional CSS and try this new code. 

.header-wrap {
	padding-top:10px;
	padding-bottom:10px;
}
.header-wrap nav {
	display:table !important;
	width:100%;
}

Button will appear below navigation, its cause you have placed button code after </nav which should be placed before <nav if you want to display button on top thanks