Although technically it may be fine to have carpet under the hearth pad, I can't imagine WHY you would want carpet near your wood stove. There is always the possibility of a burning ember popping out at some point, in fact it is almost inevitable. I imagine that would lead to small burn marks in front of the hearth and stove, which wouldn't look very nice. Maybe it takes some time for modern carpet to burn, but I would guess otherwise, it is usually nylon isn't it? Do you know what your carpet is made out of or if it is fire retardant?
Also, since you will be carrying wood to put into the stove and storing some nearby, that makes for messy little hunkers of wood, bark, sawdust, and so forth which fall off the firewood being carried and loaded. We sweep the floor right around our hearth every day, sometimes several times, depending how much wood we carry in and/or put into the stove. Wood is messy. We pulled all the carpet out of our living room before installing our stove, and we are glad we did. Consider what you track in carrying wood in from outside in the winter, or wherever you keep most of it. You sure aren't going to take your shoes off first while carrying an armload of wood. Just seems like asking for a dirty carpet to me. (I hate cleaning.)