WWYD - How late would you fly?

AngelxxRose

Long story short, my husband will be deployed when I give birth and I plan to stay with my parents at the end of my pregnancy and about a month after I have the baby.  We have two animals that we have to pay for in home care (I can't bring them with me to my parents and our dog is blind and can't handle being boarded).  It is $33/day (about $1000 month) for the in home care with sitters we trust and do a great job. 

So, I want to save money by flying to my parents as late as possible in my pregnancy but obviously want to put the baby and my health before money.  How late would you fly (as long as your OB ok's it)?  I had no complications and delivered my DD at 40weeks 4 days.  I am thinking 36-37 weeks....is that too late/crazy?  It is a cross-country flight and will be with Southwest, who allows pregnant women to fly at late as 38 weeks.  Thank you!