You shouldn't divide household tasks based on income. Hours, maybe. You both want to relax when you come home from work, obviously. But that doesn't work when people have to eat and a child needs care!
The household expenses should be combined and paid out of 1 account, with both parties contributing to that account. I don't understand why 1 person pays some bills and the other person pays others. My husband and I have separate checking accounts for certain things and I highly recommend it. If you can't work that out between you, then get a third checking account for household bills, and then you each have a small checking account for your own purchases (the other person's birthday gifts, manicures or golf dates, whatever). I have friends who do that (she also has a child from a previous marriage so her own account handles his expenses). In your case, the joint household account would pay the rent, groceries, insurance, phone and other utility bills, supplies, vacations and child-related expenses.
Do the dishes every night. Make it your time together. He cooks and puts away leftovers, you do the dishes and talk about your day together. Otherwise, he cooks, then everyone clears the table (including your child who can do SOMETHING no matter how young), and then you do dishes while your husband bathes and puts your child to bed, or plays with him since you had him at work all day. If you do dishes every day, they won't pile up and it won't be a chore. You absolutely cannot leave them for a week - food residue builds bacteria, caked-on stuff is harder to get off, and you are teaching your son not to clean up after himself.
You both work 40 hours a week, so I don't know why cleaning is YOUR job unless your husband makes up for it with other things. 40 hours is 40 hours, regardless of the schedule. So on your "day off" you have child care, right? I would set aside some weekend time on a schedule for your photography business, and have another day for family time and relaxation. If you really schedule your reading, writing, computer and editing, you'll have a lot more time free. If you just do a little every night, it doesn't seem like you have much time, you know?
You could also schedule some cleaning together if that works with your child. If your child naps, that's a good time for you and your husband to take on cleaning - my husband and I vacuum and dust together, go through the piled up mail and send the bulk of it to recycling, etc. We also grocery shop together a lot of the time. He does more laundry than I do. I do more cooking. If you have a washer/dryer in your apartment or even downstairs (vs. an outside laundromat), put in a load of wash when you get home while your husband is preparing dinner. Put it in the dryer after dinner while you are doing dishes. Then sit together on the couch after your son goes to bed, and sort/fold together while you talk about your respective days. Even a young child can learn to sort and fold clean socks, or can help sort dirty laundry by whites/colors. Get him involved early so you don't raise a new generation of people who don't keep up with the chores.
If I understand you, you work 40 hours a week in 4 days and make $200 a week? So you make $50 a day for 10 hours each day, so you net $5 an hour??? That's an awful lot of hours for little income - you might rethink that.
You both want to relax when you come home - understandable. Not realistic. If you spend more time together, you won't be at odds over whose responsibility things are - they just go faster with 2 people.
I'm more concerned that the 2 of you think that half of the car insurance is yours and half is his, you each have your own cell phone bill, etc., rather than seeing these expenses as combined family expenses that you choose, as a couple, to incur. You are also being evaluated by your hourly rate rather than the number of hours you put in. THAT'S what needs to be altered, I think, if you're going to have a healthy relationship. Bills are bills, regardless of whose name they are in. In our house, the phone is in his name, the electric bill is in my name, etc. - it has to do with who set up the account when we moved in. But it's not based on who uses the most! It's a FAMILY expense. So it's paid by the FAMILY checking account.