Amom,
There is no more or less risk adopting interstate then adopting locally. There is more paperwork, primarily with ICPC, that can hang you up. Be prepared to stay 10-14 days, and I agree get an extended stay hotel or short term corporate apartment.
FAA requires health cert for any infant under 14 days old to fly, it is irregularly enforced. Some airlines have policies that are more restrictive on age, again it's irregularly enforced so be prepared for the worst.
You can also wait to fly once TPR has been completed, rather than being there for the birth. I think that's 48 hours after birth for biological mother, biological father can sign or deny paternity at any time.
Here's the statutes from Florida:
http://www.flsenate.gov/Statutes/ind...3/titl0063.htm
HTH, hang in there. Hopefully some who have adopted from Florida can add their expertise.
Regina