Yes, it refers to cricket, with the wicket-keeper being the fielder behind the wicket, who has dedicated equipment and is frequently called on to catch the ball. The catcher in baseball is similar. It's a position requiring focus and fast reflexes, as Dickens describes. You can get a sense of the skills required of top wicket-keepers in this video.
Miriam-Webster and wiktionary have only a single definition for the term, and M-W dates it to 1750. This is probably referring to the early Laws of Cricket (see also) from that time, which already make reference to the wicket-keeper. Cricket was both popular in Victorian times and a subject Dickens was familiar with - consider the cricket match in Pickwick Papers.
So given the lack of an alternative definition for the term, and the good fit for the simile, Joe's unstable hat does demand of him the skill of a wicket-keeper, as in cricket.