When the plant is dormant (out of leaf) is an ideal time and should minimize any transplant shock, especially if the vine is still quite young and rather newly planted. In colder climates, it may be best to wait until late winter/early spring before buds emerge, otherwise fall is a fine time. Soils remain warm, rains are frequent and roots are in a process of elongation that eases the transplant adjustment. And you never want to fertilize anything that has been recently planted or transplanted - if you move it now, wait until spring to fertilize, should you need to. Mulching well with an organic mulch (like compost) will help insulate the soil for winter and offer a nutrient source as well.

Last year my other hydrangeas didn't lose their leaves until December. I think that although we're considered zone 6, it is actually much warmer here than other parts of this area (being coastal and in a protected area). The vine was planted in May but has many new branches and was rather large to begin with. I'll update my post on the progress of the transplant. Thank you for the advice.