Try going to speedtest.net and seeing how the throughput and latency (ping) compares with your sister's computer. If the numbers are reasonably the same, it's probably not an issue solvable with QoS... unless you just want to be evil and compensate by having her computer's connection be dreadfully slow to match yours so that she shares in your pain. Usually QoS, when automatically set, has to do with prioritizing certain protocols (e.g. voice/chat, gaming, etc...) but can, like you suggested, involve setting QoS for certain ports or even MAC addresses but that depends on customization abilities of your router.
All else being the same, I would look to other possibilities... If the hardware between your computer and your sister's is significantly different (or if your computer is more 'loaded down' with software that loads the CPU and RAM) it may be more of a matter of your computer taking longer to process the data especially if it has to go through Flash, different web browsers, etc... rather than pure network speed.