Which japonica are we talking about? There are quite a few plants with 'japonica' as part of their name. I suspect that this may be Chaenomeles japonica - the one with the prickles??

If I'm right, then now is a good time!

I agree, the only plant that actually uses "Japonica" as it's common name is the Japanese Quince though as Spritz has already noted, many plants have this as their species name (the second part of the scientific name, the first being the genus name) for example with plants such as Aucuba japonica, Skimmia japonica, Fatsia japonica etc.

Incidentally, any of the above including the Japanese Quince as said above can be planted now.