Sad news. It looks like Dr. Fate will not be a playable character in the Injustice Gods Among Us video game and will be relegated to just being a background prop for one of the stages. I'm taking this from an interaction I had with Ed Boon on twitter were I jokingly asked if the Dr. Fate game play was saved for next week. Mr. Boon replied with a joking tweet saying "Um... yea.... yea lets go with that", hinting that there will be no Dr. Fate playable mode, at least in the initial game. We can at least hope for a DLC pack in the future either featuring Earth 2 characters or magical characters that he could possibly show up in.
So, for now, this is all we have to look forward to of Dr. Fate in Injustice. Let's hope that changes in the future.