Seems your anchor tag is not visible as logo because there is nothing in side anchor tag.please try the below code push something in the anchor tag.
<a href="https://google.com"><img src="yourpath/image.png"></a>
Please use something like this and try it.
$(function() {
$('#menu').cookcodesmenu({
brand: '<a href="https://google.com"><img src="yourpath/image.png"></a>'
});
});