Do you know what I read from all of this: you are scared and worried for her.
I also get Autism - My son is Autistic (now young adult), and believe me I've been to hell and back. I also get the being immature for their age - In one hand my son is very mature for his age, but on the other he is a good couple of years younger than his age.
And I understand the young and pregnant - I was 'just' 18 when I had my son.
I understand the want/need to keep something familiar to your God-daughter, as everything is changing, and you are trying to hang on to the one familiar thing.
I can tell you from my experience as a young mother - her current friends WILL leave her, they say they won't, but they will. They and your God-daughter will have different priorities. I can also say from experience of others who stayed on at school who were pregnant/had a child - she will be known, not by her name, but as 'that girl who's got a kid', and will likely get bullied for it.
Do you have a teacher at school who YOU like/get honest response from? If so, approach them and ask for an honest conversation on how the school will accommodate your God-daughter. Do they think that the school will actually accommodate her, or are you on to a loosing battle?
Putting her pregnancy aside - If the school are not supportive, then you are on a losing battle (been there, done that!). You and her Mum have probably, like many of us with children with additional needs, spent her school life fighting for her education and extra accommodation for her needs. You need to look at the bigger picture and work out if this is the fight you need to take on. My own feeling here is that unless this is a school with a young Mum unit - then this isn't the best/supportive place for her.
If it was me, I'd be putting my energy into the transition to college. I understand that she wouldn't step foot into the college to see it - but you could do things to make the initial process easier - photos of the college, going by and just standing outside, meeting somebody from the college (probably many times!) so she has a familiar face etc etc