My baby is the same age as yours, OP, and is breastfed (every 2 hours during the day, more or less frequently at night depending on the night - I recognise you from the Sleep board
). My DP has a commute of just over an hour. Baby is not a great sleeper at night (I do all night wakings) but is happy to go in a bouncer, etc, when awake.
As far as I'm concerned, I'm on maternity leave, not housework leave, so DS is my priority during the day, followed by making sure I'm showered, fed and watered. When he's awake and not feeding, we play, go out, or I do housework while he goes in his bouncer, etc. If I'm really tired, I nap when he does.
We go out most days, either to groups, with friends, or just for a walk/to the shops. Fresh air every day really helps me, as does hanging out with other mums in the same position, but everyone is different. I see going out as beneficial to both of us.
In the day, I do laundry and most food shopping (some online), and try to at least prep dinner. On a really good day, I might manage to cook something for the freezer or hoover/do a bit of cleaning, but that's not every day by any means.
In the evenings, DP spends time with DS while I cook or have a break for half an hour. We take turns doing dinner depending on whether DS needs me. He gives me a hand with bath time, then clears up and has the later part of the evening to himself while I do bedtime (but will help on request; it can be a long process and is generally less fraught if I do it by myself).
At weekends, DP usually takes DS one morning so I get a bit more sleep. I usually get an hour or so to myself when he takes DS for a walk.
DP gets more free time than me, but I feel like that's inevitable at this stage. The important thing for me is that he facilitates a bit of time for me at weekends and is hands on in the evenings.
I find it massively helpful to get someone else to take DS out for a walk, as he naps really well in his pushchair and if timed right, I get a break of 1-2 hours, which saves my sanity, even if it's only once a week. Is this something that might work for you?