If the answer above is None it means there is no specific mention in the legislation, but you still need to ask local law enforcement before drinking in Falkland Islands.
It is prohibited for any adult to sell, give or provide alcohol to a minor under the age of 18 years in any public place or licensed premises. Parents may permit their children to consume alcohol on private premises. Minors consuming alcohol in public are committing a criminal offence. The law provides exceptions for the consumption of alcohol by minors for prescription of or at the direction of a government medical officer or in the course of the administration of Holy Communion according to the rites of any Christian denomination.
You can find more legal details and links here:
Wikipedia Legal Drinking Page