early spring will be fine providing the ground isn't frozen.
lift them with as much soil around the roots as you can safely lift to avoid too much root damage.

Just remember that you aren't moving so much as multiplying: any piece of root left in the ground will grow into a new bush.

Thank you both for your replies and advice, I want to put a raised bed for growing a few vegetables where the raspberries are. I'm only going to move them about 3 feet.

To keep raspberry suckers from coming up among your veggies, you'll need to wait a year, and cut and paint with SBK all the suckers that come up this year, then put down non-woven weed mat before building the beds.

Thanks Tugbrethil, I will do that. I don't think I'll get around to having the raised bed built early in the year anyway so I will move the raspberries and do as you suggest.