Each follicular unit of hair has blood vessels, glands, nerves, skin, and fat. It takes all this plus a growth center and the right genes and nutrition to make hair grow. Since by definition hair is an organ, transplanting the hair from someone else is like transplanting a heart, kidney, lung, etc.
One may tend to think that a person (a Family, friend or well wisher) with same blood group if willing to donate hair to another person should be an easy solution for people with hair loss but it is not that easy a solution!
Generally hair transplantation from one person to another (called Allogenic or Homologous Transplant) who could be living person or a dead person (Cadaveric Transplant) carries the similar risks as organ (liver, heart, kidney) transplants.

Transplant from the animal fur to human head is called Heterogenous or Xeno Transplant. There is a

1. Risk of rejection and failure
2. Wastes money and effort of surgery
3. Lifelong use of anti-rejection medication that could lead to further health complications
4. Transmission of some diseases.
5.It involves surgery on the donor as well
6. There are medico legal aspects to it besides ethical issues: such as possibility of people selling their hair for money in future.

Dr Orentreich in 1972 reported that the transplanted hair can survive for at least one year. However to prevent graft rejection steroid must be injected into the grafts every 30 days.
So this is possible but not practical.

Such experiment has been done before without success. More on blog