Depends on a lot of things, like whether it's a sculpt or a digital scan, when the new Doctor's look is decided, and when licensees will have access to promotional and production imagery, and so on.
If it's a digital sculpt, they'll be waiting in a queue for a spot in her busy schedule to get the scanning done. If it's a physical sculpt, they could start at any time. Last I heard filming doesn't start until early in the new year, so it could be quite a wait on being able to get started on the outfit, and who knows ultimately how easy or difficult that will be to achieve once they do start.
Big Chief might want to shoot for as close to the new series launch as possible to maximise hype and potential pre-order sales, but the earlier they go the less they will have to draw on in terms of possible accessories and any potential exclusive pack in items. So unless they are willing to put up something for sale with 'additional accessories pending' or some such, I'd guess they wouldn't launch until end of series at the earliest, or perhaps more likely, during the run up to next year's Christmas special (presuming that is still a thing).
Of course that's all just speculation on my part, and Big Chief's actual choices aren't always, let's be kind and say, predictable. So we'll just have to wait and see really.