Evidently , there is quite a bit of interest in the new Kindle Oasis. On the Amazon’s Kindle Forums, customers are already reporting ship dates for some models pushed back until June. Earlier today, I was already seeing “Due to popular demand, some configurations will ship after April 27th. See the latest shipping dates at checkout” notices on the page.
From what I am reading, the issue seems to be tied into specific cover color choices and whether or not you want the no special offers option. The no offers version seems to be the one with a later ship date. Here’s a tip if your color option is in stock and you don’t want to delay delivery: Order the special offers version and see if you can pay Amazon to remove the offers after the fact. On every Kindle or Fire that had special offers included, Amazon has allowed customers to pay a fee to opt out. The Kindle Oasis isn’t listed yet, but the device is not technically released.
Here’s the Amazon page with instructions for removing special offers.
The eBook Evangelist 
I just got a notification that my delivery date has changed from April 27th to September 6th! September!!!
I cancelled. That’s just ludicrous.
Wow! Did you double check with customer service to make sure the email was correct before canceling? That sounds like an awfully big jump. That’s comparable to the original Kindle wait times!
ETA: Was this a new order or a change in shipping dates to an existing order? In my response above, I was thinking of an existing order, not a new one. They seem to be pretty popular. I haven’t checked shipping dates recently, but that is a still a big jump from June to September. 😦
Same thing happened to me. I too canceled the order. Ridiculous! I wanted it for my summer vacation reading.
Kim, I think a lot of people saw it the same way! 😦