To answer your first question: Yes. There is nothing illegal about a pregnant woman leaving the state without notifying the biological father (especially because it sounds like the parties are not married here).
As for the support 14 years later, that's a bit more complicated. You don't have an obligation to pay support until paternity has been established. This can happen in several ways. The simplest way is if the parents were married during the pregnancy. Also, the parties could have signed a voluntary acknowledgement of paternity at the hospital or birthing center where the child was born. Finally, the mother could have filed a paternity suit, known as a "filiation," and the court could have established paternity. From your post, it sounds like the third option is most likely going to be the one that will happen (there will be a court case and most likely genetic testing as well).
Until paternity has been established, you have no obligations (such as support) towards the child, but you also have no rights (such as visitation).
Once paternity has been established, you have the responsibility to contribute to the support of the child, even if there is no court order requiring the payment of a certain amount of money. If there is a support order, the amount may be increased or decreased by a court or administrative order. The support order may be enforced by wage withholding, tax refund intercepts, property liens, and other involuntary processes. The child may have the right to inherit from your estate and receive Social Security benefits based on your earnings. The child will also be given access to your medical history.
After paternity has been established, you will also have certain rights of your own. You will be able to seek visitation. You will also be able to seek custody (but, after 14 years and having never known your child, this is unlikely unless the mother is an unsafe or otherwise very bad parent).
Unfortunately, you don't have any remedy for the lost 14 years. Also, you cannot voluntarily relinquish your parental rights to get out of a child support obligation. The only idea I have here is if both you and he mother agree to someone else (her husband) adopting the child and you relinquishing your parental rights. You cannot do this without her agreement and if this were in in Oregon, a 14 year old child is old enough to have a say in it as well. You really need to speak with a Florida attorney to find out the laws of that state. It probably wouldn't hurt to post your question on Avvo's Florida section as well.
Here are some links where you can learn more about paternity in Oregon, but remember, the mother and the child live in Florida, so you will need to become familiar with the laws of that state or hire a Florida attorney:
My responses to posts on AVVO are not legal advice, nor do they create an attorney-client relationship. In order to provide true (and reliable) legal advice, an attorney must be able to ask questions of the person seeking legal advice and to thus gather the appropriate information. In order for an attorney-client relationship to exist, you and I both have to agree the the terms of such an agreement.