I just travelled to Canada with an eight month old and honestly it was awful. Even though I booked a basinet seat I didn't get one, and then on the second flight they said it was meant for smaller babies.
The baby cried for 15 hours straight. Honestly, if I were you fly your mom, or whoever you are seeing here to Qatar it is soooooo much easier.

And if you try to put the baby on the floor he will just crawl away...unfortunately the lap thing is what you might be stuck with.