Yep, this has been me twice now. We moved here when I was pg with my second and knew basically no one. My family all lives across the country. But in the several months we lived here prior to the baby's birth we definitely made a few friends that I could have relied upon to be there for us if needed. I worked hard at reaching out to the parenting community and getting involved during those months so that I would maximize my chances of having support available. Now I'm pregnant again and moving again! This time I will only have a couple months to make friends, but I'm really crossing my fingers that it will happen. When are you due? Do you have some time to sort of network and get involved?
Another idea is to hire a doula specifically for childcare. If you have some time, you can meet with the doula and have her get to know your kids and vice versa- play at home, play at a park, etc. Doulas are used to being on call day or night and are fine being around birth so it can work out really well.
Good luck! I hope things work out easily for both of us!