photos please?
I have no idea what poppy you have but I can tell you that I'd heard so often that poppies must be sown where they're to grow - and that they cannot survive transplant... that I was scared to try. Well, I had to move a little less than 2 years ago and potted some of mine up, crowded in the pot 'cause I expected them to die - and it was July and August and kinda hot. Well, some lived and some died. But, most lived. I'd also brought some seed from them but the plants gave me a much quicker spring welcome just seven months later when seeds would not even have sprouted. Since you ARE moving, nothing ventured, nothing gained. Dig all you can, start with the smallest, never allow them to dry out, get them in their new home as quickly as possible.

I was struggling to rememeber the varieties I brought, afraid I'm a bit of a dunderhead. All I can remember is; California poppies (of course!), Maltese cross, and a big peach one with black blotches.
GH-

Papavers (poppies) come in Annual and Perennial varieties. Since you bought the original poppies and planted the in your garden, I would venture to say they were likely perennial poppies. They come back from roots ever spring and they can also reseed themselves, but are not invasive. Perennials transplant well. Annuals do not. Annuals need to be sown directly where they will grow. I have divided & moved my big red-orange Oriental poppies several times with no problems.
Iceland Poppies ( Papaver nudicaule ) come in shades of radiant white, yellow and orange, like this one:

Here is a link that might be useful: Poppy ID website.