I'm so sorry about your dog.

I had to have my dog put down and it helped me to think that at least she had a full lifespan and didn't get taken young. I'd sort of known that one day I'd lose her. It doesn't make it any easier when that day comes, but at least it isn't a huge shock.
So a parakeet isn't really what I had in mind as my next pet, if I decide to even get anymore pets, that is.
If you catch and cage it and bring it indoors, you don't have to keep it. If you don't find its owner, somebody will adopt him if you put him up for adoption. They are fabulous little birds, real little characters. Somebody will want him, I'm sure.
I also wonder if the parakeet will have the sense to fly south when the weather is starts to get cold. If it was a pet I don't know if it would, OR instinct could take over. Not sure. I do know that if it stays here it will die with the cold winters we have here. Any comments about that anyone??
I don't know anything much about migration. I just have pet birds and most of the birds around here seem to be here all year round.
Anyway, I think migration is done in flocks, isn't it? They all go together and stick together so they don't get eaten/attacked/whatever. He's got no flock. He's also not "local" insofar as escaping from snow goes. If he's been a pet, he won't have the slightest clue about the requirements of surviving in the wild, including moving somewhere warmer. What do the bluejays and starlings and those other birds do? Do they migrate?
This article suggests they migrate the other way around, I've no clue what that means for a bird completely on his own and in a different hemisphere to "home", but it doesn't sound like he'd know what to do.
http://www.ehow.com/info_8127580_migration-habits-budgerigars.html
Although he's been ok so far with the small birds, it just takes one bigger bird with an attitude problem and he'll be history. I really would try to get him inside and safe.