So I just went on the website now after trying multiple times when the site initially 'opened' and after taking a break to do some gardening and I was able to order the Minnie plush.  As soon as my ordered was processed, I went back to check and it is now sold out.  I am doubtful that I will actually receive the item and will mostly likely get an email from 
Shop Disney indicating that the item is unavailable for shipping or something like that 

.
ETA:  Okay, so I checked again and it is saying that the mug and plush are available.  Either they are releasing the items in waves or this is likely just another website issue.  I think I will stick with my original hypothesis that I am probably not going to end up with the plush after all...lol.