Did Moses establish Jerusalem as the capital of the Nation of Israel?

No, Moses did not enter the Promised Land. He died before the people of Israel went into Canaan to claim the land.

(Deuteronomy 34:5 "So Moses the servant of the Lord died there in the land of Moab, by the Word of the Lord.")

It was King David who established Jerusalem as Israel's capital, 2900 years ago.