Insurance After Job Resignation

Contemplating resigning from my job within the next couple of weeks due to stress while pregnant. (Due late March) my husbands insurance open enrollment period isn’t until June, but according to their office manager, special enrollment can be considered for a spouse due to “loss of coverage”. Does anyone know if the loss of coverage still counts if I resigned and wasn’t terminated? He has BCBS & we’re in Texas.

Additionally, if I can’t get on his insurance- should I start shopping the market on healthcare.gov now?

Is COBRA still offered when you voluntarily resign from your job? If so- How much should I be expecting to spend? Would it be worth it to do COBRA for the duration of my pregnancy to keep the same benefits rather than shop the marketplace until I can get on my husband’s in June?

I am obviously a novice when it comes to anything related to health insurance and I have no idea what I should anticipate spending monthly. I’m just trying to plan ahead. Any advice/knowledge helps!