I would say it took a full year for me to have sex normally, without feeling different or careful. I had a straightforward birth with a full term baby, with internal stitches. We had tentative sex after the 6 week check (well, to be fair, if anyone called that actual sex I would be surprised!) just to get over the hurdle, if that makes sense. Then left it for a couple of months because, y'know, fuck that. 
I had no libido whilst I breastfed, but enjoyed a bit of non penetrative stuff now and then, mainly for the closeness and the connection with our old life. I had PND (not very severe) and found adapting to the loss of our life as a couple v hard. This helped me feel like life would be normal again some day.
DD was (and for her age, still is) a terrible sleeper. It fucking ruins you, doesn't it? So sheer exhaustion got in the way of my libido as well. DH would have been business as usual, but let me get there in my own time.
So a year to feel the actual physical normality, but realistically 18months to having any kind of normal sex life. Even then, there is still a 'sex night' and the understanding that I am going to sleep straight after! Spontaneous, pre-baby sex is still MIA after 2 years, for the most part. But we have always been intimate to keep close.
Sorry, this is an essay! I just wanted to be honest because you can't talk about it in real life as openly, I am sure!
The rea saviour was a night away here and there. I took the support of people who would just have DD and put up with no sleep until we got back. It really, really helped to have a full night's sleep and then a morning together. Waking up in the same bed and just having a chat. If this is in any way an option, take it.
I think you are right to try to fix this. It's reconnection and protecting your marriage. Set aside an evening, beg a babysitter for even an hour, and talk to him.
Good luck x