I think the early years of parenting are very hard on a couple. I can only encourage you by saying that children grow up so fast and soon your child (DD or DS? - not sure) will be off to school, playdates then packing his own school bag etc, then making his own lunch and so on and so on.
Someone once said to me that "the days are long but the years are few".
If you want some feedback I can make my following observations, based only and your post and the experiences and my friends and I - many of who are now divorced (me included so no judgement from me):
Firstly, the name calling from him is unacceptable and he should not speak to you like that. Has to stop immediately. Raise it in your counselling, as a non negotiable. He can be upset with you but not disrespectful to you. Also it's a terrible example to set for your child.
Domestic labour - just review it all - go through all the jobs and just split them so that everybody gets a reasonable amount of time to themselves but there is also enough family time together. If you can afford it, certain jobs are easy to outsource. If not, you might just have to de-prioritise certain jobs until your child is bigger. That is quite normal in families with young children. There just has to be some give for a bit.
Your issues with the changes to your body - what are you doing about this to try to boost your self confidence? Do you have a lack of time for self care? Do you spend too much time on social media comparing yourself to others? Have you dropped some activities that you used to do that used to make you feel good about yourself? Just some examples - stabs in the dark.
When it comes to your body confidence, the impact on your sex life - what changes would YOU like to make? Are you being fair in the sense that have you truly considered that your sex falling off a cliff is really difficult for the party in the relationship that perhaps misses that aspect, and how things used to be. No one is entitled to sex - pestering is unacceptable - before I get jumped on; but just saying that it can really hurt if one party feels rejected in that way.
Your overriding instinct to make everything about DD at weekends etc is quite a lot of self inflicted stress and in a way is not inclusive, for want of a better word. Perhaps your husband feels left out / isolated - hence just disappearing off for gym and hair cuts. If he works full time he will need some weekend time to himself BUT you can also incorporate family time into the schedule, perhaps starting by asking him if there is anything he wants to do or making some suggestions for an outing.
Spending all your weekend time with your mum friends makes for a pretty lonely weekend for your husband. There is no way I think he wants to hang out with your mum friends and their kids, so what do you want him to do instead? Have you articulated this to him? I think you should mix your weekends up. Hard to balance I appreciate but I do think you should intentionally reserve some weekends for FAMILY time (not just mum and DC time).
Not seeing what you do, not appreciating you - these should be raised in your counselling - you don't feel valued but I bet he doesn't feel valued/appreciated either. A 3rd party can help you to see each other's perspectives.
Finally, I don't really see anything from your post about you 2 making time for each other as a couple. No mention of nights out together, date nights, booking a babysitter or taking turns with friends so you can have some adult times to yourself as a couple. There is a chance that your husband feels overlooked as well, pushed out maybe, not appreciated for working full tiime - only you can tease out what the reason is - and that can only really come from him.
A lot of us forget that before the precious DD/DS there was a couple, and the couple relationship is just important as the DC relationship. That relationship needs to be attended to as well. So many of my friends and I got so caught up in being there for our beautiful DC (which is as it should be, some might say) but the cost can be high.
You need to talk to him and your counsellor and you need to prepare for those chats so you articulate yourself properly, but you also need to be prepared to hear his side of the story. There is a real chance that he actually genuinely misses you and time with you.
Alternatively, if he is just a man baby who hasn't adjusted to parenting life (of which there are many), you will find out soon enough because you will go for counselling and not much will change - either in the form of changed behaviours on both your parts, or increased understanding of each other's contribution to the family unit. And that road leads to just more and more distance between you.
I really hope you can work it out. Divorce / separation is awfully painful. Ask me how I know.
Good luck.