OP I only got though reading half the replies on this thread so apologies if someone has told you all this amongst the ill-informed and uncaring responses.
I'm a single mum and have a lot of experience of mediation and family courts.
Everything needs to be framed around the child's best interests. Parents have responsibilities not rights. Bear that in mind when putting your case forward to your ex or to the court, if it comes to that. You need to be able to reasonably argue what you are proposing will be best for the child.
The 4/4 model isn't workable longterm. It might suit the father. He could argue it suits your DC but it doesn't suit you for the reasons some PPs have stated, because you would have to manage your life around his shifts. Therefore it's not a solution that allows you to work and plan your own life to support your DC. The courts will tend to look at how the week splits so those saying 4/4 is 50/50 and workable aren't being helpful. A child needs consistency and certainty, and a different schedule every week doesn't support that.
I suspect he's saying he wants 4/4 to be difficult because you've said you want to move, but wanting to have things his way isn't centring your DC. As you've been told, he won't need to pay anything in maintenance if you have a 50/50 arrangement, so that may also suit him.
You need a longterm solution. DC is small now, but any contact arrangements that start now set a precedent, so you should be thinking about what happens when your DC is at school. It will be difficult to argue cutting down contact with your ex further down the line.
50/50 isn't the starting point for small children and IMO isn't the best solution for little ones. To the PPs suggesting a week on, week off, no court would order that for a 1yo. The court is more likely to award more time to the primary carer, perhaps with a view to that changing as the child gets older.
Mediation probably won't resolve this if there isn't a compromise to be reached and it may end up in court. I think a lot of people who haven't been through mediation misunderstand what's involved. Mediators aren't there to advise. They are there to mediate without taking sides.
If you can afford a solicitor, find one who can give you useful advice and support. That might not be the first solicitor you speak to.
I can underatand why you want to move nearer your family but unfortunately it isn't straightforward and would mean a lot of travelling back and forth for the whole of your DC's childhood. You would need a strong case if you wanted to propose to the court that you move away and be the resident parent with majorty care, such as a job etc that would allow you to provide a better life for your child. I'm sure you feel trapped by that but this is the unfortunate outcome for a lot of people when relationships break down.