As an F1 student, you should have insurance, right?  Make sure you add your spouse to the policy.  Since you know you are having a baby, pick the best option with optimum coverage and low deductibles.  I am not sure you will qualify for Medicare as you are foreigners.  So, it is best to have insurance.

You should consider post-partum care as well.  Certain states have free clinic and WIC (Women and Infant Care) program.   You can actually get coupons from WIC to get certain food items for free at the stores.  Check with Health and Human Services office to see what help you can get for your wife and the baby when the time comes.

Just to be safe, there is no need to mention to the airline or the immigration about your wife's pregnancy.  There recently was a bill in congress about not allowing automatic citizenship to the babies born in the US.  I am not sure if it passed and became the law.  I heard lot of Chinese who have valid visas come to the US to have the baby in order to get American citizenship.  So they might be getting stricter on that front.  So best to keep this to yourself during your travel.

Good luck!