Yes, but as a general rule your passport will only be valid until your 22nd birthday, as you must first apply to retain your Danish nationality beyond the age of 22. This is also known as the “22-year rule”.
The 22-year rule refers to Danish nationals born outside Denmark and who have never held residence in Denmark, who may lose their Danish nationality on reaching the age of 22, unless they apply between the age of 20 and 22 to retain it. See below on how to apply for a Certificate of Danish nationality. Once you have received your Certificate of Danish Nationality from the Ministry of Immigration and Integration in Denmark you can apply for a full 10-year passport.
If you were born outside Denmark, are below 22 years of age and you have resided and been registered in Denmark for a continuous stay of a minimum of 3 months, you will have retained your Danish nationality and thus, a full 10-year passport may be issued to you, without a Certificate of Danish nationality. Please consult your Embassy to check whether you are eligible to a 10-year passport beyond your 22nd birthday.