What is the most common and shorter way to say this? (shipping date)
Please let us know the date when the goods will be ready for shipping.

Is there any special expression which describes this status?
Is it a shipping status or a production status?

Question

What is the most common and shorter way to say this? (shipping date)
Please let us know the date when the goods will be ready for shipping.

Is there any special expression which describes this status? 
Is it a shipping status or a production status?

Answer

Your original statement is better as “ Let us know the date when the goods will be ready for shipment.” or “... ready to be shipped.”

But it’s important to note that “ready for shipment” doesn’t mean they will be shipped then, only that they are ready. The “shipping date” is the date the goods are shipped.

Answer

This is referring to production status. It means the time when the products are ready to be shipped.

Answer

Please let us know the date when the product has shipped.

I would also add:
,and please provide the tracking information.

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