Under the provisions of the Child Abduction Act 1984, if your daughter's father has parental responsibility you can't take your daughter out of the country without his permission. The only exception is that, if you've got a residence order, you can take her out of the country for a maximum period of one month at a time.
If her father does not have parental responsibility you're free to take your daughter abroad (for an unlimited period) without his permission.
Your daughter was born before the date when her father would have automatically gained parental responsibility by jointly registering her birth with you. So he will only have parental responsibility if:
(a) you were married to him at the time of your daughter's birth ; or
(b) you've entered into a formal parental responsibility agreement with him ; or
(c) a court has granted him a parental responsibility order.
If he does not currently have parental responsibility, he can still apply for it, through the courts. The criteria used in assessing such an application are summarised in this link:
http://www.direct.gov.uk/en/Parents/ParentsRig hts/DG_4002954
Confirmation of the rules imposed by the Child Abduction Act can be found here:
http://www.ips.gov.uk/passport/apply-child-rul es-parental-responsibility-rules.asp
At 16 years old all young people have the right to walk out of the family home and, if they so choose, never to have any contact with their parents again. (If their parents reported them as missing, and the police located them, the police would be barred from revealing the young person's location to their parents). So it follows that your daughter will be free to