My first transaction using Bitcoin-Qt
I'm assuming it's because it's never caught up with where my transaction is on the blockchain. Is this correct?


Yes.


  I can see when I take the address and look it up online the transaction of receiving the funds I just can't confirm a balance.


That's normal, if your client is still synchronizing.


  When everything does sync can I only transfer my balance out using the same app?


No, it's possible to use a different Bitcoin wallet. You need to 'export' the keys in your wallet to another program. See How can I export the private key for an address from the satoshi client?


  Also I had to replace my hard drive on my mac recently so I took both the Bitcoin app and the Library/Application Support/Bitcoin folder and put them on my new hard drive, are there any other files I would need to get access to my balance?


Is there a file inside there named 'wallet.dat'? If yes, then you have what you need to spend your Bitcoins. If no, then no.