I had a little Beagle mix and she went everywhere with me including to school with me...and I would put her in the plane as I was doing my training...that being said,
if you're careful you may convince them to feel a 2 G turn or experience a power on stall. One of my former girlfriends was terrified by flying, she needed a Xanax or Ativan to fly so I was surprised when she came along with me in a little Archer. she experienced, slow flight, 2G turns and touch and goes. Afterwards, she lost her fear of flying, no more meds, and when it came time to travel she would say I was on a 767 or I was on a 737...etc.
the epilogue would demonstrate that she subsequently went Sky diving!