Materials science isn't my thing, so I don't know how long such tests should take. A LiveScience piece from 19 October said the following:
"The owner of the papyrus fragment has been making arrangements for the next round of analysis of the fragment, including testing by independent laboratories with the resources and the specific expertise necessary to produce and interpret reliable results," [Kit] Dodgson [director of communications at Harvard Divinity School] wrote. "This next phase is likely to take several weeks, if not months."(Noted recently on Facebook by Andrew Bernhard.) I suppose we are still within that time frame, so it's not fair to be too impatient yet. I hope this does not deteriorate into an endless round of delays, as with the fake metal codices.
Background on the Gospel of Jesus' Wife is here and follow the links.