I deleted my wallet.dat file -- wondering if an exchange I stored my coins on might have a backup so I can recover my coins?
I think you are confusing something.
The wallet.dat is a local file on your computer, exchanges usually have nothing to do with it.
I assume data recovery software would be the thing you need.
We need more details to offer a better help:
So you've send Bitcoins from an exchange to an software wallet on your PC (bitcoin-qt?), corrrect?
Why and how did you delete the wallet.dat?