Unless you make an attempt to address these issues by booking with discount codes that waive either the additional driver or underage fees (or both), adding your daughter would subject you to both the additional driver fees (~$10/day) and the underage driver fee ($~15/day).

The USAA (if you have/can get a membership) and AAA discount codes (if you have or can purchase a membership) will waive the additional and underage driver fees (subject to some limitations). More info on avoiding underage driver fees is available in this FT thread and in our blog article here (and this blog article announcing new benefits of the AAA discount code).

I am not 100% sure whether either of those codes (or others) would waive the underage fee for additional drivers (depends how the systems are programmed), but you certainly could make an argument that they should at the rental counter or to post-rental customer care if you use those codes and are charged the underage fee for your daughter.