I'd wait until spring. Warm season grasses like Miscanthus enter a period of root dormancy in late summer or fall which makes dividing them late season somewhat problematical. Since the roots are not in active growth like they are with many other plants at this time of year, it is iffy whether the division will take over the winter. For best results, I'd wait until late winter or early spring when new growth begins and you typically do your cutting back for the season.

Ditto with your proposal to snag a clump of J. blood grass from the restaurant planting in another thread :-)

Do what the Miscanthus is doing: chill. Wait until Spring when success should be guaranteed.

Definitely give it a Spring dividing,they all seem to take their time rooting and settling in,likely won't achieve full height the first Summer,but....wouldn't you rather move when the weather is only going to get better?