Executing these lines of code:
Avatar a = new Avatar ();
Debug.Log (a.name);

results in NullReferenceException. The name of a newly created avatar should be the empty string or something else, but not null.

Is the Avatar actually getting created? For example, running this code:
Avatar a = new Avatar ();
Animator an = new Animator ();
an.avatar = a;

also results in exception when assigning the Avatar to the Animator.