Mr' Jonathan responded, hie thee to Google, and ye shall find.
In summary, Urusalim is attested as far back as the 19th century BCE, and repeatedly in the El-Amarna letters in the 14th century BCE. For reference, Avraham Avinu was born in the 18th century BCE, encountered Malchitzedek King of Shaleim (which is today called Jerusalem) in the 17th century, and the Exodus was in the 13th century.
Why the dual form Yerushalayim? In short, nobody knows. It was a choice of the Masoretes, so it was comparatively late (early Middle Ages), and we don't know why they did it. Perhaps it was a reference to the two cities: the old one below Har haMoriah, and the new one built to the north and west, approximately where the current "Old City" is today on Har Tzion.
* on another list.