In response. Yes.
In Hinduism and Buddhism, the Buddhas are both male and female, i.e., they are depicted as both female and male gods. Guan Yin, the Chinese Goddess of Mercy, is a male god in Hinduism. And Guan Yin, like her “male self” in Hinduism, can appear in many forms of living beings. This is recorded and described in both Buddhist and Hindu texts.
Reincarnation is not gender specific nor gender constant. A male or female can reincarnate into a female or male. It depends on which birth the “remixed” bundle of instincts, according to the Tibetan Book of the Dead, wishes or chooses to reincarnate into. Intentional perpetual existence of a spirit in a corporal living form dictates the reincarnation. A spirit that has not accumulated sufficient merits (Buddhism) or good karma (Hinduism) will not reincarnate into a higher level of a living being. A person that has accumulated bad karma or has done bad deeds in life will reincarnate into a lower life form, like a man who stole money will reincarnate into a domesticated water baffulo in life-long servitude to his former victim or the family from which he had stolen money from (Chinese fable).
There are essentially two forms of spiritual perpetuation: to reincarnate as a human being to accomplish a goal and leave a legacy in the living world, or to reincarnate as a living being to create living offspring who will perpetuate the ancestral spirit. This is borne out by the fact that the offspring of good ancestors usually live a good life. One example is the many generational offspring of Confucius. The 73rd generation of Confucius is a government official. In Buddhist causality, those who worship the Buddha or donate generously to a Buddhist temple reincarnate as high ranking officials since high ranking officials generally enjoy a life of relative wealth and prestige.
Male dogs generally do not take care of the young and in Chinese folklore, male dogs are lonely wonderers and vagabonds. Female dogs care for their puppies and puppies recognize only their mothers, therefore, the perpetuation of the ancestral spirit through the living offspring is achieved. And for a spirit of a lonely vagabond male dog that had lived a lonely wondering life, reincarnation into a female dog would achieve the goal of spiritual perpetuation through her offspring.