Don't pump the water from the old pond into the new. Trash pumps will transfer small fish. You would defeat the purpose of killing off the old pond. Kill it off, then just let the water of the new pond rise to meet the old.
That pond looks pretty small. You might be able to use hydrated lime to do the job and not need to hire someone to do it with restricted chemicals (not that there is anything wrong with doing it that way). The process involves "shocking" the water with a high enough level of Ph that the fish do not survive. There are old threads here on PBF describing the process. I have not done it personally though.
