I'm guessing that you're rather young, right? I only ask because if that is the case you need to make sure that your mother is on the same page as regards having birds in the first place. I'm so sorry that your budgies flew away. I know that must've been a hard blow. But before you get another bird you should do two things.
First: Try your best to find your budgies. As was mentioned earlier, it is quite possible they have been found... or that they will be. You owe it to them, and to yourself, to at least try to find them, right? You can start by making flyers and posting them up in local supermarkets and such. Also, get the word out with your local police department, veterinary offices, rescues, anywhere someone might conceivably go to surrender a found bird.
You can also post on Facebook, and sites like Petfinder.com. Heck, you should post right here! We have quite a few Australian members in this community. Believe me, there are stories of people on this very forum who have found their birds even over a month or two after having lost them. It does happen.
Second: If you have exhausted all possible means of finding your budgies and have met with no success after another 2 or 3 months, you might want to have a discussion with your mother about getting a cockatiel. I suggest that you read this link together:
What Students Should Ask Before Getting a Bird. - Parrot Forum - Parrot Owner's Community as well as this one:
http://www.parrotforums.com/new-mem...friendly-warnings-keep-your-parrots-safe.html Why? because you both need to be on the exact same page about what getting a bird can mean. And you should both also discuss how your budgies were lost. Something like that can't be allowed to happen again. (And there are so many other dangers that a companion parrot might face.)
I don't say all this to point a finger about what happened with your budgies. Accidents happen, of course, and I'm sure you and your mom feel badly enough about it. No judgement, here. I just want you to take a beat or two before moving on to your next bird.
All that done, then feel free to check out our Cockatiel sub-forum. You'll find tons of valuable info there.