The problem as I see it is that because you are claiming to exercise Treaty Rights as a self-sufficient person, you cannot use the Surinder Singh route, where specifically the exercise of Treaty Rights must either be as an employed person or self-employed person.
Accordingly it appears that the only way of getting your wife (as she will be) to the UK wll be to apply for a spouse visa, under UK immigration rules. And that means that she will not be in the UK exercising EU Treaty Rights.
Therefore she will not have a document listed in 3a :-
An EEA family permit, residence card or permanent residency card issued by the UK Home Office; or (except in the case of an extended family member)
-: and therefore I cannot see how she can qualify as an exempt person.
3a? Go back to the very start of this topic, indeed to its very first post, then click on the link therein.
But is it important that your wife qualifies as an exempt person? Being qualified from a medical school in Austria, will she have any problem registering in the normal way?