Learn Danish: Jeg vil gerne have en kvindelig læge.

In Danish, vil gerne means "would like to" and needs a verb to follow it. Because you are asking for a noun (en kvindelig læge), you must use have (to have). Literally, you are saying "I would like to have a female doctor."

How does the word kvindelig relate to kvinde?

Kvinde is the noun for "woman". Adding the suffix -lig turns it into the adjective kvindelig, meaning "female" or "feminine". This is a very common way to form adjectives in Danish, similar to adding "-ly" or "-ish" in English.

Does the adjective kvindelig change depending on the noun?

Yes. Because læge is a common-gender (en) word, kvindelig stays in its base form. If it described a neuter (et) word, you would add a -t to make it kvindeligt. If it were plural or definite, you would add an -e to make it kvindelige.

Are professions like læge always gender-neutral in Danish?

Yes, almost all job titles in modern Danish are gender-neutral. Læge means "doctor" regardless of gender. When you specifically need to state the doctor's gender, you simply add kvindelig (female) or mandlig (male) in front of the noun.