Shifting a full size gorse would be a rather prickly challenge but moving a small one should not be a problem. Is this your bog standard common gorse or a fancy one?

As Moon Grows has said ok when they are small if moving a large shrub I would reduce all branches at least by half and try and keep a large root ball as possible keep well watered the following year make sure you plant same depth .

Wraping in a old blanket and tie with string will help with not getting scrached to bits

Blanket wrap to move, is a brilliant idea. When you move it remember that all varieties require a poor, well-drained sandy soil in full sun. Best of luck!

Gorse does not necessarily need a poor soil to grown - that is the niche it has in nature...

Under the gorse is hunger and cold,
Under the broom is silver and gold.

Just don't over-do the mulch and feed as it is not necessary for gorse to grow and flower - that's all!