As Senator Dickson was still a senator, the office of the Black Rod was responsible for assisting parliamentarians at the funeral. It was not a state funeral. The Black Rod's office also assists when former senators pass away, and it assists with the funeral.
In terms of parliamentarians, I must admit I don't know if it's ever happened. I've never been requested to assist in the funeral of a parliamentarian or a sitting parliamentarian. We do work closely when it is, again, a state funeral, such as for Mr. Layton, or things like that.