Hello, Kennedy,
You may see "Spanish tutor" on my profile, but I also have bachelor's and master's degrees in music and have taught piano and voice for many years. On WyzAnt, I have mostly been tutoring Spanish, but since I recently relocated, I am ready to do more online music lessons.
Yes, the dominant (V) chord of both major and minor keys is the same. This is because in the case of minor keys, the chords are usually based on the harmonic minor form of the scale, which has a raised 7th degree. Using your example, the 7th degree of both the D major and d minor scales would be C#. The dominant chord would be A major, A C# E (dominant 7th, A C# E G).
The function of the chord in the key doesn't matter, it's the relationship to the D major or D minor scale that determines it.
Key of D major or D minor: A is V
Key of G: A is V/V
Key of F: A is V/vi.
I hope this helps! Let me know if you have other questions.
Best regards,
Elizabeth