I have a post on my blog
with directions for this 4.5 inch sock.
If the actual foot is 4.5 inches long you might want to make it a little longer. The one on my blog is knit with regia and size US 2 needles. If you wanted it a little bigger, you could go with a size US 3 needle and some sport weight yarn or cascade fixation.
The post explains the changes you need to make to the tropical punch slipper sock pattern on the free pattern page (link at the top of my blog).
Hope this helps.