RAW depends on whether or not your table considers weights of monsters.
The case for only 1/2 movement
Most monsters in the DMG do not have assigned weight values. Because of this, Jeremy Crawford on Twitter has simplified the answer as to moving grappled creatures to size only:
The rule on moving a grappled creature (PH, 195) works regardless of a creature's weight. It cares about creature size. [...] The rule doesn't rely on weight largely because we don't specify weight for most monsters.
The case for applying push/drag/lift rules along with 1/2 movement
But we do know approximately how much these dinosaurs weighed and a DM could utilize that - but they do not have to.
If they do, then what's going on here is the interaction of two separate rules: those for grappling and those for pushing/dragging/lifting. We need to look at each and how they work together to answer this.
The rules on pushing, lifting, and dragging state:
Push, Drag or Lift. You can push, drag, or lift a weight in pounds up to twice your carrying capacity (or 30 times your Strength score). While pushing or dragging weight in excess of your carrying capacity, your speed drops to 5 feet.
Size and Strength. Larger creatures can bear more weight, whereas Tiny creatures can carry less. For each size category above Medium, double the creature's carrying capacity and the amount it can push, drag, or lift
The Quetzalcoatlus has a strength of 15 (as noted) and is also Huge, which means it's maximum drag/lift weight is 1800lbs. Because the weight of the Brontosaurus exceeds that, your movement is dropped to 5'.
Dragging/Lifting/Carrying a Grappled creature
This answer covers this, but to summarize, the language for grappling states (my emphasis):
When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.
This specifically states the terms drag and carry which are the mechanical terms described above and should therefore still apply. Your movement is still halved, so you'd only be able to move 2.5 feet.