I have a mac that I never use, would storing my bitcoins on a wallet on that laptop and then only connecting it to the internet when I am ready to transfer money be safe? Is there any reason not to do this?
Your laptop needs to catch up every time you want to make a transaction, which is not good.
The ideal solution would be Bitcoin Armory, which is designed for this type of thing:
How to sign a transaction using only an offline computer?How to sign a transaction using only an offline computer?
Find the mac version here - but note that it's in beta, hence why it's not on the main site.
Would I get an error from the P2P network or would I have duplicate coins
The second time you spend the coins, other nodes will reject it.