I went back part time when my very similar dd was 11 months, it was extremely hard and a period of time I have tried to blank out of my memory tbh!
I do remember dd would happily have one big nap per day. She also liked the car and the reclining buggy but didn’t get long sleeps there.
But she didn’t seem to “need” that the recommended amount of sleep at night, and the night waking is really hard going.
I decided I had to stop bf, so I weaned dd - she refused to take a bottle so it was straight to a sippy cup of baby milk and at that age, I figured fair enough as almost old enough to be on more substantial solids diet anyway.
I also did some gentle sleep training although it didn’t feel gentle on me at the time but eventually I was able to shush her to sleep (dh never had the patience to get very good at it, so it was mostly down to me).
What’s the routine going to look like when you are working, thinking about childcare and your hours etc? The nursery my dd went to was magical - they got her to sleep on a little soft floor mat with all the other babies.
So I think the truth is your baby CAN learn and you can teach better sleep habits, a month is about enough time to get something to start working and one day all these sleep issues will be a fuzzy memory.