Is having a copy of my wallet.dat file enough to recover lost Bitcoin? I have been using Bitcoin-qt to mine bitcoin. I am a little worried about losing my coins on my computer, so I have made a backup of my wallet.dat file and put it somewhere safe.

Is this the right way to keep my coins safe from my computer crashing? Am I completely on the wrong track? What else might I need? I haven't encrypted my wallet.
Yes, but having the wallet.dat file is only enough to recover the lost bitcoins if it hasn't been compromised in the meantime (that's why it's a good idea to encrypt your wallet). There have been at least 2 other questions in the last week or two where a user tried to recover an old wallet and found it had been emptied.

If you do encrypt your wallet (and you should, to protect against malware stealing it), then you'll also need your passphrase for the wallet when you want to restore it and reopen it.