If you dont trust her, then I would say she should not be your girlfriend.

First what came into my mind when reading your question is why should you care? You apparently do not know - just suspect her (for whatever reason). 

If you do not plan to cheat on her so you are in no 'danger' and your girlfriend, provided she really did that, will probably feel happy and satisfied.

If you however plan to cheat on her so you shall decide if you tell her (I would find it very naive but you may have different point of view) or you will try to do it secretly (being ready to face then all the consequences which it may bring).

If you then plan to cheat on your girlfriend secretly so searching for your eventual candidates on Facebook profiles sounds a bit inefficient ...

There are much better and more efficient ways how to find your alternative lover (or one night stand if you are into such dangerous hobbies).

But I do not expect you mean your question seriously anyway

you set up a fake facebook of her ideal mate and play the same game, fair play trickery, equality to the max.

There is a good way of solving that problem. You climb up to the roof of your building and jump down to the floor. When you hit the bottom you will feel happier and your girlfriend will delete her fake facebook page.

I take it since you ask about six random topics every day that this is a hypothetical question.

Who cheats on Facebook? That is just stupid. Facebook is blocked to 99% of the population. Get a smarter girlfriend. Better yet, make a fake profile yourself and cheat with your girl friends fake profile.

I would report her to autorities for braking the law