My site currently looks like this:
I want the navbar and logo to be more similar to the style shown at willynillie.org.uk (Essentially a bigger header, with some text next to it, and the navbar to be a bit further down).
How do I make this happen?
I hope you are well today and thank you for your question.
You can style the header however you want by developing custom CSS code and adding it in the Custom CSS option of your theme on the below path.
Admin Area -> Appearance -> Customize -> Dazzling Options -> Other -> Custom CSS
To display some text nest to logo you will have to develop some custom in the child theme of Dazzling theme by overwriting header.php file of theme.
Do you want to apply exact styling on your site as this site willynillie.org.uk?
Could you please share me your site URL which is accessible for me so that i can help you to achieve it?