It would be a little difficult to simply replace the image that is currently on your web page with a Juicebox gallery.
The image you refer to is not displayed with a standard HTML <img> tag but is actually a background (set via CSS) for a <div> which contains other content (such as your navigation menu).
If you replaced this <div> with a Juicebox gallery, then you would lose all its content.
I would recommend that you keep the 'header-wrapper' <div> in place, remove the background image by deleting the following entries from the #header-wrapper section in your styles.css file:
background: url('../sydney-wedding-photography-images/sydney-wedding-photo-video-sydney-harbour.jpg');
background-size: cover;
background-position: top center;
background-image: url(../sydney-wedding-photography-images/sydney-wedding-photo-video-sydney-harbour.jpg);
... and embed your Juicebox gallery (following the instructions in the Embedding Guide) below your <nav id="nav"> or your <header id="header"> section.
I would recommend that you embed your gallery using the baseUrl method of embedding as documented here. This method of embedding allows you to keep the gallery files inside the gallery folder and you would upload the entire gallery folder (not just the contents) to your web server. Also, it does not matter where on your web server you upload your gallery folder to as long as the paths within the embedding code (the path to the 'juicebox.js' file and the baseUrl itself, pointing towards the gallery folder) are correct.
As an example, if you have a gallery folder named 'my_gallery_folder' and you upload the entire gallery folder to your web site's root directory, then you would be able to use the following embedding code. (This code could be used in any page throughout your web site without modification. The leading slashes in the paths denote your root directory.)
<!--START JUICEBOX EMBED-->
<script src="/my_gallery_folder/jbcore/juicebox.js"></script>
<script>
new juicebox({
baseUrl: "/my_gallery_folder/",
containerId: "juicebox-container",
galleryWidth: "100%",
galleryHeight: "600",
backgroundColor: "#222222"
});
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->
If you want to leave your current home page in place whilst you try things out, just make a copy your 'index.html' file (in the same directory) and use the copy as a work in progress.
Your 'header-wrapper' <div> currently has a fixed height (the image does not scale when you change the browser window's height) but is responsive horizontally so to do likewise with your gallery, just give your gallery a fixed height and a width of 100%.
I hope this helps.