The answer is yes - if its been in situ less than 3 years, otherwise you risk breaking too many roots. Best time is usually late November and December - but you may lose any incipient flowerbuds present, waiting to open in spring.

I agree with Bamboo, if yu have to then now as it is still quite mild. But try and dig as much of the root ball as you can. the soil that you excavate for the new home can go in the hole it came from.

It will be heavy lifting job so try and get some help and take care of your back.

Cannot see from photo if it is in a pot, but as camelia flower so early in the year, I would wait until after it has flowered before moving. This will prevent interruption to the flowering in case you break too many of the fibrous or main roots, and will give the plant a good chance of recovering during spring. Keep it well watered for a few weeks after moving, and top it up with potassium based feed during early summer. Camelias also like a lime-free or slightly acid soil, so chuck in some ericaceous compost when you move it, if your garden needs it that is?! You also need to be aware that it needs a slightly protected spot in your garden, as any sudden sharp frosts not wind protected will cause flowering buds to suddenly drop. A fleece blanket may be a suggestion.

Thanks Bamboo, Sbg and Avkq, notes taken.