What is it you're wanting to take?
Is it viable to dig the entire plant out (make sure you've a nice big rootball) and take it with you? I did that with some mature rhods and they survived!

It might be easier (and quicker) to buy new trees though :)

If you're moving house, the new owners have bought the garden too, as it was when they viewed, unless specific plants have been excluded from the sale, so you can't just dig up whatever you want from the garden and take it with you.

If you're moving soon there's nothing to lose by trying cuttings now, though I think you're likely to have more success later on in the year - summer, maybe.

Are you going far away? Perhaps you could ask the new people if you could come back later on in the year for a few cuttings - they might be prepared to take a walk round the garden with you, holding the plastic bag that you pop the cuttings into? Then they could be sure you aren't wrecking what is now their garden and you could discuss the neighbours who (we hope) are now mutual friends. ;-)