If she really wants to learn, chances are that she probably can, and don't worry quite so much about causing her pain or making her vomit. I have had pain from DT'ing, but nothing severe -- in fact, I wouldn't say it really hurts any more than having vaginal sex with a thick cock.
I have never vomited from DT...I always pull back long before that can happen. If I have gagged a few times, and think there is any danger of my actually throwing up, I signal my husband and we take a break.
Your cock is quite a bit thicker than average, vanir23. This will make it significantly more of a challenge for your girl to DT you. My suggestion is that you obtain a dildo with about a 5" girth, made of some relatively flexible (not rigid) material, and have her begin practicing with that.
Lying on my back with my head off the edge of the bed was an excellent dildo-DT-practice position for me. I followed some advice I saw on the internet, and would just insert the dildo as far as I could without gagging. If I gagged, I would pull it back, relax, and start over. The article I read said that once you start gagging while trying to learn, you should pull back -- if you continue to try to DT the object, and especially if you try to move/thrust with the object, you will only gag more, and this isn't about training yourself to gag. It's about training yourself
not to gag.
Unlike some other posters, I really do not like DTing an actual cock in head-off-the-bed position. In this position, the man being deep-throated has all of the control over the activity -- the receiver has virtually none and cannot move his/her head away if a problem develops. Our two best DT positions are: (1) Him on his back on the bed with his legs apart, me on my knees between his legs facing him, and (2) Him standing and me kneeling in front of him.
When I do non-DT oral sex, I usually keep my hands submissively behind my back (sometimes they are bound there). But whenever we DT, I insist on having my hands on his thighs, so I can push away if I start to gag or something. This prevents us from ever getting close to me vomiting -- I have enough control over the situation to signal him by pressing on his thighs with my hands. That way even if he is holding my head or hair, he can let go and pull out in time to avoid disaster.
Several years ago, I wrote a couple of long blog posts about my journey in learning to DT. If you and your girl are really that interested, you may find my experiences helpful. Here are links to the two posts:
How I Learned to Deep Throat - Part 1
How I Learned to Deep Throat - Part 2
This post may also be a good read for a woman wanting to expand her oral skills:
Women and Fellatio
Hope some of this helps.