Cream does last quite a while in the fridge, especially before it's opened - it has a pretty high fat content. So you may be able to buy it when you can, and still have it around when you want it.
Failing that, honestly, I think that anything you can do with milk and additives is probably not going to be nearly as good as actual whipped cream, so you might as well fall back to another substitute: aerosol whipped cream. If you get a decent one that's actually made with cream (not milk and oil and stabilizers, like your Dream Whip) it'll probably still taste better. And I'm pretty sure it lasts a really long time (months?) in the fridge even once opened. (But I don't have any to check for sure.)
As for actually making Dream Whip: as mentioned in several comments, it has a lot of ingredients that'll be way harder to find than cream. Sure, they're probably shelf-stable and you could probably buy them online, but it'll be a lot of trouble, and it might well be more expensive than just buying the Dream Whip itself. It's possible that there's a more home-ingredients version (I'm no industrial food authority), but unless you have some more restrictions I don't know about, I'd still prefer the other alternatives I suggested.