The Washington Post had an interesting piece about whether it still makes sense for the government to mint pennies, given how much they cost to make relative to their value. The article might have asked the same question about the dollar bill. Coins are in general much cheaper to keep in circulation than bills, and given that a dollar today is worth about as much as a quarter was 35 years ago, it might be time for the switch.
Of course we do have dollar coins, but they rarely circulate. In this respect, it's worth noting that the last two dollar coins both feature women (Susan B. Anthony and Sacagawea [a native American woman who accompanied Lewis and Clark on part of their journey]). These are the only U.S. coins or notes to portray women.