Last November I was able to add an additional driver at no charge thru Alamo..not sure whether it was because of QS membership or because of the discount code I used (which I don't recall). I booked online and it showed up as a feature. Great experience renting thru Alamo at the WDW Car Care center.
I don't know if QS entitles you to an extra driver but if you use the Sam's Club code you get an extra driver for free. It shows up on your reservation.
If you are a member of Costco their codes get you free addtional driver. You can go to their website and click on Travel at top of page. Look for car rental along side bar on left, click and brings you to the discount page. I also recommend getting their travel book instore, it has coupons. I used the costco ID and coupon and got 2 discounts - the discout for costco members and the one free day. It included the addtional driver. Play with the codes and search mousesavers.com for more codes. I used the Alamo codes as they worked best for me and they have dropped recently. Also, they have last minute discouts too so keep going back - they can get lower as your dates get here.
Have a great trip!
If you don't have a Sam's or Costco membership - the Walmart code (430710) does add a second driver too. I also don't know if QS does, but I don't think so...
I rented from Alamo last April. I used the wal mart code for a discount AND an additional driver. I also used their online coupon for an additional discount and paid $215/week total for a brand new 2006 Cadillac DTS.
Good Luck,
Joe