If the dollar is pegged to gold, then gold would not fluctuate in dollars at all. It would, however, fluctuate in terms of all other currencies not either pegged to gold or to the dollar. Which it does anyway.
Sure it would. You can say that one ounce of gold can be exchanged for $1000 U.S. dollars but elsewhere in the world the market price of gold will fluctuate with supply and demand.