Hi! I was trying to come off of Paxil two years ago for a few months. The effects were so bad: dizzy, nauseous, vertigo, anxiety, etc. When I got down to 5 mg it was unbearable, so my doctor actually put me on Prozac to wean me off since it has a much longer half life. That only took 2 weeks and I was fine during that process! Good luck!
If 10mg is working for you, it's not a low dose -- it's your dose. Which means you're metabolizing the drug and therefore, given this is the most difficult of them all to stop taking, your decision to ignore your doctor was a good one, in my opinion. The speed at which you taper off is determined by how you feel -- if you start getting withdrawal symptoms that are too strong for comfort, then you slow down the taper. You go as slowly as you need to. And remember, not everyone gets withdrawal -- you might get none at all. As for your doctor, he's violating the basic rule of do no harm. I wouldn't use this doctor for your mental health medication needs anymore.
I would like to add what you already know and that is cold turkey and low dose is a matter of opinion. Yes 10 mg is "low" but our bodies all react differently. A good doctor should work with what you are comfortable doing. After all, we know our bodies better than anyone.
I would advise your doctor of what your plan is but at the end of the day we all do what we believe is best for ourselves, which you already began to do. I would let him/her know your plan but I wouldn't worry.