Why doesn't the IAU consider Quaoar to be a dwarf planet? Only Ceres, Pluto, Haumea, Makemake and Eris are listed by the IAU as dwarf planets. Quaoar is bigger than Ceres, yet it doesn't make the cut. In fact, it fits the IAU description of a dwarf planet


  The shape of objects with mass above $5 \times 10^{20}$ kg and diameter greater than 800 km would normally be determined by self-gravity


since Quaoar has a mass of $1.4 \times 10^{21} $ kg and a diameter of 1110 km.

Futhermore, light-curve-amplitude analysis shows that Quaoar is indeed a spheroid.

Why isn't Quaoar considered to be a dwarf planet by the IAU ?
It probably is a dwarf planet. (It almost certainly is a dwarf planet.)

The naming procedures at the IAU are that "Objects that have an absolute magnitude (H) less than +1 [...] are overseen by two naming committees, one for minor planets and one for planets.  [...] All other bodies are named by the minor-planet naming committee alone." source—wikipedia

Quaoar has an absolute magnitude of +2.4, so it has its name approved by the minor planet committee, and that committee doesn't rule on whether it is a dwarf planet or not.  

It's just procedural.  

So it's not that this is a particularly controversial object: It's big and round enough to fit the criteria for a dwarf planet. It just doesn't have the stamp of approval from the planet naming committee, and they don't get out bed for anything with an absolute magnitude of more than +1.

As observed in a comment, officially naming objects or putting an official box-label on a particular object may not get a particularly high priority in the scientific context. What an object is referred to is what gets established in debate and an "official" discussion and label is only be granted in particularly controversial cases of great general interest