Old joke and logical fallacy

It's just unclear language that could be interpreted as an implicit argument, but should really be left as an unfunny joke.

If you want to be a logical fallacist, you could interpret it like:

P1) One can live with AIDS for 10 years with no problem

P2) I have AIDS (if she gets her wish)

C) I will live for 10 years with no problems

This is the appeal to possibility. It's also possible she will die before then, from either AIDS complications, or something else. The disease won't magically get her to 100; she has to survive both it and anything else that could kill her.

It is also an example of the ambiguity fallacy as 'problems' is not clearly defined; we do not know whether she is referring to problems arising from AIDS, or anything else.

The joke is that if she gets AIDS, she will live for 10 years without any problem, thus becoming a centenarian. The 'logic' of the joke fails because of the above.

I think the confusion comes from cutting short the entire premise which is
" One can live with AIDS for 10 years with no (AIDS-related) problems '. 
Since the ' AIDS-related' phrase is something that can be reasonably inferred, it can be omitted.
So I think it's just poor communication which leaves however an open space for joking - and I have to admit I found it pretty funny. No need to apologize for enjoying black humor ;)