Chances of finding a job with a January start date in Dallas area?

I graduated in April in Utah and am 27 weeks pregnant. I’m due in November. My husband and I would love to move to Texas to be closer to family before the baby is born. Unfortunately his job will not allow him to work fully remote from another state. He has been searching for a new job since March and hasn’t been able to find anything. If we want to move before the baby is born, we’d have to move by the end of September, and he’d need a job offer by middle of September.

His current job can allow him to work 3 months fully remote before terminating him. So if we move at the end of November, he could work until the end of the year while continuing to job hunt. I’m considering the possibility of beginning work in Texas in January, as much as I would hate to leave my newborn. I considered substitute teaching, but I know it wouldn’t be enough money to support my family. How easy is it to find a full time teaching job in the middle of the school year?