OK, I'm going to play devil's advocate here to add a bit of balance. You sound lovely, and bright, and you are in a stable committed relationship,and both you and your partner seem to be honourable and ambitious, and well-intentioned but...
You say all young mums are assumed to be single, in a council house and on benefits.
Um, sorry but you are, in fact, single (i.e. unmarried)are you not? And at only 18 with a baby, statistically your relationship has a slim chance of going all the way. Sorry. You are both students, so unless you have private trust funds or very generous parents we must assume that you are not, for the next couple of years at least, financially self sufficient and are therefore claiming benefits of some sort. If you intend to resume your degree any time soon your child will need full-time childcare - who will pay for that?
Unless you live with your parents you are, presumably, renting a house/flat with the help of housing benefits of some kind. It doesn't matter whether it's a council house or a private let - it's who funds it that's the issue here. Unless of course the baby (and all the paraphenalia that comes with having a baby) and the rent and household bills, and anticipated childcare costs are being completely funded by you both on the back of your student loans and your partner's holiday job, without claiming anything other than your family allowance. In which case I apologise, and take my hat off to you.
You say (with a hint of smug indignation)that your partner is working 'flat out' through the summer - well, so he should be. There are no pats on the back for working to support your own child I'm afraid. Choosing to have a family means being a real grown-up, and working 'flat out' in one form or another, for the next twenty years, and that's without bringing the unfinished degrees into the equation. And every teenage mother trots out the old chestnut about 'fully intending' to go back into full-time education to have the career she always intended to have, to support her child, as soon as she is able. Blah Blah. Very few do. Babies are a full-time job in themselves, as you will learn. To get you both through the next two or three years (minimum) both graduated, relationship intact,and without some form of reliance on the state purse will be some kind of miracle. You probably think I'm being a cow. I'm not a cow - just a realist. But I'd love to see you prove me wrong. Good luck. and congratulations.