The word for deer and the word for prosperity are homonymns in the Chinese language. Deer often represent prosperity in art. Also, legend has the deer living a life of a thousand years -- thus, they deer is often association with the god of longevity. 

Lingzhi (灵芝), also known as the glossy ganoderma, is the sacred fungus of immortality that grows on the trunks or roots of trees including the pine.
The lingzhi does not decay like other fungus but instead becomes woody and thus can survive for a long time.  For this reason, it has become associated with longevity.
It was also believed to grow on the "Three Islands of the Immortals" where immortals lived. Deer are reputed to be the only animals able to find lingzhi.  Deer and  crane are sometimes shown holding the lingzhi in their mouth.