Not a good thing to happen.
Thats a small M/T , Im assuming that the M/T had no tang on the end? Though they are not designed to be a driving tang, they can save your quill, if the M/T doesnt hold. Ether way, your in a spot now you must do somthing to fix the problem.
The first thing I would do, have a look in the quill with a good light. If the damage is minimal, then you could do a few things. Clean up the taper with a stone, and get all the hurt spots off it, if you have a spare, use that to check . Inside the barrel of the quill, you should be able to see the damaged spots. being yours is a small M/T , it could be hard to deal with comared to a larger one.
You can attach very fine grit sand paper to a M/T arbour, and with light pressure, turn it and keep a close eye on the bore, and the sand paper. The sand paper will show where the damaged area is..
If you go slow, and recheck the fit as you take the bad area down, you could get it fitting, and have it hold again. Yes , you could buy a reamer, and that would centainly work, but unless you have used one before, you could make matters worse.
If at all possible, locate the damaged stot, and work only with that. If inspection shows one spot, then work only on that spot. You dont want to get the quill sanded out of round either. Work with caution is in order.
If your quill can hold arbours with a tang on the end, by all means do so. Ive added tangs to arbour that didnt have them, its not hard to do.
If when drilling holes that you fell could get the arour to spin in the quill, then you could make a clamp to retain the drill from spinning, or as simple as snapping on a vise grip positioned in a way that if it did spin, its not going far, and not going to gouge up the quill in the process.
One other thing to practice. Wipe the quill clean before you insert your arbour, also wipe the arbour clean aswell. These should be clean, dry, and oil free before inserting them.