Who's the expert, you or him?
Cleaning the carpet after it has been laid not only makes more sense due to the fact that it will (hopefully) be secured around the edges, but there's also the risk of the carpet getting dirty between you cleaning it and it being refitted.
Tell your mate to get it fitted properly by someone who knows how to fit axminster carpet.
The dog hair isn't a problem. First of all go over the carpet very thoroughly with a groomer, in several directions, to loosen it up a bit. Then vacuum with a good strong upright vacuum cleaner, first across the pile and then facing the same direction as the pile points.
That should get rid of quite a bit, the rest will come up with a rotary and bonnet which you should use between prespray and extraction. If you still have hairs remaining after extraction, give it another quick groom and whizz the bonnet over it again. The remaining hairballs should come up once the carpet is completely dry.