I'm so sorry to hear that things are tough. Like you, I found the first few weeks of having a baby impossibly hard.
I agree with others that it's totally up to you and your husband what works for you, and it's no-one else's business. It's great that your DH is being really supportive - he sounds really hands-on which is great. As long as he's ok with it, don't let anyone make you feel bad about it. And do try to keep talking to each other about how you're both doing/feeling.
Have you and DH considered shared parental leave?
I do think you should chat to both your GP and HV about whether you might have post-natal depression/anxiety, or be at risk of developing it. One in ten women do (including me) - it's surprisingly common. It's an awful thing to have to go through - but there's loads of support that you can access via your GP, so please do use it if you think it would be helpful. It would also be worth getting all the blood/urine tests for various other conditions eg iron/anaemia etc.
As well as being a lot less mentally stimulating than most jobs, looking after a baby is really draining both physically and emotionally. Different people experience it differently. For me, with PNA, the first 6 weeks of having a baby were the hardest thing I've ever experienced.
Baby clubs and socialising are really valuable and I'd strongly recommend getting out as much as you can. But they won't resolve PND if that's what you've got (only medical support can do that). Plus you might find it hard to get clubs in the first place, if you are suffering.
Incidentally, extreme tiredness is a symptom of PND/PNA. So if you were suffering from that, it would be all the more necessary to let your DH do night feeds until you get better (which can happen quite quickly once you get help).
I'm sure some people will slate me for such a PND-heavy post. But it's worth looking into, at least.
I'd also strongly recommend joining the July babies thread in the post-natal section of MN - there's loads of lovely ladies waiting to give you moral support!
Obviously all the above is just my thoughts - you need to do what's right for you.
Sending you virtual hugs.
Tobebythesea and ineedwine - hope you're doing ok / feel better soon.