Quaoar was discovered in 2002 and has a Moon orbiting named Weywot which was discovered in 2007.  He's about half the size of Pluto and it takes him an average of 287.5 years to orbit the Sun once. Quaoar's orbit is very circular compared to Pluto and other newly discovered planets and also got only a "slight" tilt - all of this indicates that his influence is a more harmonious one. 

 

Astrology: 

Quaoar talks about the natural order of life and its creation laws and asks to respect the natural order and laws - to take responsibility and to live in harmony with these laws.

He seems to have liberating and governing aspects, that may ask us, to use our own abilities to create order under the natural/universal laws, which includes honoring and respecting all life.  

Also he influences the evolutionary path with "overtone", due to his long orbital time. 

 

orbital cross / points: 

Perihelion  14° Aquarius -  Aphelion 14° Leo

Northnode 13°46' Virgo -  Southnode 13°46' Pisces 

most north and south same degrees Sagittarius - Gemini

 

Mythology: 

According to Tongva Myth, Quaoar came to Earth and found chaos and felt pity. He started to dance, whirl and twirl while he sang the "creation song". He sang two other "gods" into creation and they together created the Sun and the Moon and then all 5 together created everything else existing.   (Reference: en-academic.com)