I'm going to go against the grain here and say I thought the Doc was interesting, rather than unconvincing.
To me, her chief trait was that her thinking was unable to deal with ambiguity. I could well believe that a child growing up with parents who themselves may have that trait, and therefore themselves converted to a an extremist religious position - a chief benefit of which is to offer simplified solutions and a clear narrative as to how to live a life in a nuanced world with reduced ambiguity - would grow up with a similar mindset.
Moreover, add into that a sense that she is not loved by those parents, that they see her as 'failing' them - then you get a child who is trying to both adopt and rebel against that mindset. So you get extreme attention-getting behaviour and rebellion, alongside an extreme mimicry of behaviour her parents 'approve of' (early pregnancy, outside of marriage, but determination to prove she can succeed).
And I could well believe that she would look for something that would allow her both the approval and sense of family that she seeks, alongside something that recognises her 'exceptionalism'. As well as providing a narrative that resolves complexity and ambiguity into simple 'either/or', 'right/wrong' decisions.
So I quite liked the character. In some ways, she was there to demonstrate how radicalisation is a resolution of trauma and a desire to resolve the ambiguities of the experience of living with the Western promise of self-actualisation - and that has been conjoined with a narrative demonstrating the increase of fundamentalist religion more generally (and what those fundamentalist religions offer to modern people).
As other posters have said, the series necessarily homogenised a number of narratives of radicalisation - and that does lead to difficulties. But then, i suppose each narrative of radicalisation is both unique and, at the same time, has certain structural similarities with many others.