The airlines I fly typically do not guarantee the whole family can sit together. They will try and ensure one adult is sat with the child, but with the child does not mean beside, it could be the row in front or the row behind.

Qatar use Altea as their dispatch control system. This comes with theoretical seating which kicks in at T-72 and does what it can to keep people on the same booking seated together the best it can, but that will depend what seats are pre selected by customers who can preselect for free or have chosen to pay.

You have called the call centre looking for a reassurance the whole family can sit together. Unfortunately, on the ticket you have purchased, they were unable to give you that assurance.

If you want ensure the whole family to sit together you will need to purchase seats. If you want to make sure one adult is beside the child and less worried about where the other sits then that will probably happen.

I think most adults would feel uncomfortable sat next to a child without a parent beside them, which means these issues can often be sorted out on board. How would depend on the seat pattern on the aircraft.

My opinion is that if you choose not to pay to select your seating then ... one adult and child together with the other adult close, possibly together.

Its highly unlikely that, by the time you depart, all 3 of you will be scattered in individual seats around the cabin