Do you think $3,000 plus an income of $1200 a month will provide for a baby?

I have about $3,500 saved up and my boyfriend and I will make about $1,200 a month combined income plus a little help from our parents. So in nine months that'll be like $10,000 to start out with (taking out money we spend for necessities and prenatal care along the way) and then I'll stop working so it'll be that plus about $800 a month maybe more.
I realize babies are expensive. I realize that emergencies happen, and I realize that I should've been more careful if I wasn't financially ready for a baby. This baby wasn't planned.  I don't need a lecture. I've done the math and I think it will last me at least the first few months of the baby's life if not more and then after that I can maybe start working part time. I'll also be going to school or online classes, not sure yet. 
So as a general idea, I realize we'll be struggling but I feel like I've done a good job of planning and I already have a budget all set up- do you think this can get us through a bit? I'm so stressed out and working my ass off already. 

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