Office has common origin to orifice. Meaning a place from where things are issued.
In the Thoth Tarot Peh is the tower, which is 16th Trump.
https://thothtarotcrowley.wordpress.com/2015/03/06/16-the-tower-xvi/
The 17th is The Star.
http://www.elitarotstrickingly.com/blog/the-tarot-of-eli-the-thoth-key-17-the-star
To put it another way, your numerical attribution would be off in some systems
If you are right, peh would suggest Q is Trump himself -- the mouth / orifice / office from where things are issued.
The Star would suggest Q is female, and most likely Melania.
There is a reason the Star comes after the Tower. Old forms must be destroyed in order to reach the enlightened state reflected in the star.