First, you need to adjust the image itself. You can actually do that with WordPress.com by putting ?w=180 at the end of the image link like this:
http://beckaroona.files.wordpress.com/2012/06/becca0.jpg?w=180
Next, "#branding" isn't the right selector for the Blaskan theme which you are currently using. If you view the page source, you'll see a section like this:
<header id="header" role="banner">
<figure><a href="http://blog.beccarose.co.uk/" title="Becca Rose" rel="home"><img src="http://beckaroona.files.wordpress.com/2012/06/becca0.jpg" alt="Becca Rose"></a></figure>
What you're trying to do is override the image that is set there and set an new on using CSS. You can do that if you hide the img tag and then set the resized image as a background on the link that comes just before the image. Try updating the CSS to the following:
#header figure a img {
display: none;
}
#header figure a {
background: url('http://beckaroona.files.wordpress.com/2012/06/becca0.jpg?w=180') no-repeat;
display: block;
height: 196px;
width: 180px;
}