I traveled throughout my entire pregnancy. Definitely check with your insurance 1) to confirm your coverage outside your "home" area and 2) locate medical facilities within your network.
I made a medical summary to keep with me while I travelled and left one in my desk at work.
On the header, I had:
Emergency contact information
Contact Information for my Midwife
Due Date
Date of Birth
Blood Type
Current medications
Allergies
Then, I kept a running summary of the results of my prenatal visits. It puts your pregnancy "history" in a short form that makes it easy for a care provider to see how your pregnancy is developing. Most recent results first.
weight
urine results
blood pressure
P.S. If you're flying, check your specific airline, but in general you can fly domestically until 35 weeks. You may want to get a note from your doctor confirming your due date.