No, Bitcoin will not replace Dollars. Bitcoin only will be a secondary payment option since most of people in the world even dont know to operate a computer in developing countries.
Bitcoin has already replaced dollar in the deal of worlds most expensive pizaa so there are many bitcoin users who prefer bitcoin over dollar or other fiat currencies but I dont think bitcoin will vanish the dollar or any other fiat currency. On individual level, bitcoin has already replaced our fiat currencies (at least online).