Go to Manage My Booking on the QR website. It should give you an option to upgrade your itin (outbound, inbound, or both) to business class. That is effectively paying to upgrade your fare and comes will full benefits (e.g. lounge access.) I suspect this is what your travel agent is quoting you as well.
There is also the option to upgrade within 2 weeks of your flight - this allows you to upgrade individual segments. It tends to be more expensive than the previous option and you don't get all the benefits (e.g. no lounge access.) DoD is the most expensive of all, ranging from ridiculous to infinity.