We recently replaced all the carpet in a rental house. Home Depot had a similar $37 installation deal, but I'm sure they make it up on the price per square.
Home Depot quoted us $2052 for materials plus $404 labor plus $200 for rip-up and haul away and another $200 for miscellaneous stuff like carpet rails and installing on funky stairs. It added up to about $2700 after rebates for 104 square yards (that's 936 square feet) of what we thought was very nice carpet
, for a rental house.
I also had a private flooring company come out and bid on the job. Their initial bid was almost twice as high, and they resorted to a bunch of high pressure sale tactics like "this price is only good if you sign today" that made me angry. After some back and forth between the installers, each one claiming they would beat the other's price, we ended up around $2400.
Looking at carpet samples, we saw very little correlation between price and quality. Carpet costs for otherwise equivalent products (as measured by face weight, PAR rating, pile height, warranty, etc) seemed to vary by about a factor of two. Shop around.