You are still in shock and so is your partner. That little being you carried and loved for 9 months is not with you. Hormones alone will play havoc with your emotions so soon after giving birth, much less the bereavement you are currently dealing with.
It is a bereavement as it feels like the death of all the hopes, and dreams you had for that little being you carried. You need time to grieve, to cry and to learn to live with what has happened to your child, your future family life and your relationship with your partner.
Another child at this point in time would not be fair to anyone, least of all the new child, as right now you are all in a state of flux and turmoil. Neither is a pregnancy so soon after the last the best idea, simply because your body needs time to physically gather within itself all the nutrients and strength required to make a human being. (Think of how we are advised to take folic acid for at least 3 months before trying to conceive). If you do want another child, you owe it to yourself to be physically and emotionally as healthy as you can be before commencing another pregnancy.
From a callous, practical point of view, social services could interfere in ways you don't want if they feel you haven't fully resolved all your feelings and emotions towards this child before having another. They could jump to conclusions and make choices you don't agree with .
Take the time to get some REAL professional help to cope with your feelings and answer ALL your questions re your child's disability. If offered medication to help you in the short term, take it. Make sure your partner does the same.
The two of you may find you disagree about your child's long term future (you may eventually want to care for child yourself and find your partner does not or vica versa). Many relationships run their course when a disability enters the equation. Before having a second child you need the security of knowing your own relationship will weather the storm, and that any choices you make over this child's future (adoption perhaps?) are ones you can both live with in the long term. These aren't choices you can make while you are still in shock, you need time to let it all sink in.
5 weeks is no time at all in the 18-25 years it takes to raise a chilld from birth to independence. You had 9 months to get used to a reality that was brutally snatched from you and altered beyond comprehension overnight. Time doesn't heal all pain, but it enables us to learn to live with things. Please, please give yourself the gift of time.