*SPOILER*
No it wasn't real. The ending completely gave it away.
1. The captain couldn't see the faun when the little girl was talking to it.
2. When she was dying from that gunshot, she finally imagined she was there in her palace. But then the scene goes back to her dying, indicating that she was imagining it. She never went anywhere.
3. Remember, the little girl was fond of books and stories. She simply created her own. The little girl is living in one big fantasy story.
4. Also, at the end with supposed father king. The lady sitting next to the king was her mother, but remember her mother had died. She was also holding a baby, no other than the little girl's brother of course.
The movie was executed very well.
*SPOILER END*