My little girl was born at kemh in 2011 3 months early. She was born due to PE and my placenta was not functioning as it should have. (Absent end diastolic flow) they estimated her weight to be higher than 900 grams but when she was born she was 850 grams.
Pack a hospital bag just in case and have it in the car. I got caught out at my antenatal check up and ended up delivering via c section that night.
It can all happen very fast. A few things I wished I packed were comfy pjs, breast pads, and maternity pads that weren't like surfboards like the hospital provide lol a nice handcream, toiletries (I felt like death so wanted to look decent for visitors, although none came apart from hubby and my and his mums) and a notepad and pen.
If you can, ask to see the special care nursery. They should be able to let you look thru the doors. When bub is born it's most likely going to be connected to monitors and have leads running all over it's body. Machines will be beeping and flashing, don't be afraid to ask the nurses (as many times as you like) the same questions " what's that whys that doing that" etc
We were in the nicu and scns past her due date because she was born at such a low birth weight and was so early.
I am not sure being close to term (37w) if they'd give you steroids for bubs lungs. But if you show signs of needing them (delivery any earlier than 32w) then they will give them. Craig knows that he's doing, he delivers a lot of prems (and full termers) and looks after mums so well.
Best of luck! I hope you can hold on longer.