I had high hopes when we decided to get a cleaner, but it has been a nightmare. I have tried multiple and they have all been unreliable and caused more trouble than they were worth, so I have now given up :-( On the cleaning side I now just lower my standards and blitz the house with everyone involved about once a month.
Work from home if possible - much easier to keep on top of laundry, dishes etc.
Supermarket deliveries, or go with the little one in the trolley if they enjoy it (mine did, and still does aged 4).
Fit in whatever chores you can with your little one - e.g. going to shops, bank etc. Make it normal for them to be with you/help as possible so you aren't stressing about trying to get things done.
Cook large batches - left overs for the next night, or freeze if possible. I also like slow cooker (reduce the liquid, as it doesn't evaporate off).
Tidy, mop spills, put things away as you go. Don't let it all build up and become overwhelming.
Make sure you and DH are on the same page re drop off/pick up etc, and share childcare when they are off sick. Be prepared when first starting nursery for a lot of sick days.
And again...lower your standards, particularly at the beginning! It will be really tricky to start with, particularly with nursery bugs, but after a while you'll get into a new routine!