For the 4.5 years she's been there, she's attended Uni full-time, worked part-time, received some student loans, and also received about 800 dollars a month from generous relatives in the US. Living in London is unbelievably pricey. The father does have a decent full-time job and is willing to provide whatever support he can for the baby.
I'm thinking since her baby isn't due until September, and I think her visa expires a month or so sfter graduation, it may be her best bet to just go to sign up for graduate school therefore extending her student visa, then when the baby's born I guess she could apply for the 30-60 month right to remain as a parent of a British citizen. I know she would not go on the public dole, but I'm assuming the baby would be covered under NHS.