Hi Alex,
Currently, the product listing page doesnt support filtering products by passing a search term in the querystring. However, the product listing page does support filtering Products by Category by passing the category id in the querystring.
For example:
http://www.airsoftguns360.com/Home/tabid/38/Default.aspx?categoryid=1
When the category id is passed in the querystring the products will be filtered by category. Following your example if you create categories as "brands", this will allow you to create your own separate brands or category page using the DNN Html module with links or images that filter your products by brand in Smith Cart.
Hope this helps!