18 it is. The below listed codes are obviously not complete but it is enough to verify that you can carry at 18 years of age providing you complete the application process and are approved.
TITLE 11
Crimes and Criminal Procedure
Delaware Criminal Code
CHAPTER 5. SPECIFIC OFFENSES
Subchapter VII. Offenses Against Public Health, Order and Decency
§ 1441. License to carry concealed deadly weapons.
(a) A person of full age and good moral character desiring to be licensed to carry a concealed deadly weapon for personal protection or the protection of the person's property may be licensed to do so when the following conditions have been strictly complied with:
TITLE 1
General Provisions
CHAPTER 3. INTERPRETATION OF STATUTES
§ 302. Definitions.
In the construction of this Code and of all other statutes of this State, unless the context requires a different meaning:
(3) "Full age" means the age of 18 years or older.