My last back up of wallet.dat was from the beginning of the year. My computer crashed recently and I don't have the most recent wallet.dat after receiving bitcoins. If I use my outdated wallet.dat, do I lose the new bitcoins I received?
If you made more than 100 transactions and individual receiving addresses combined, yes.
Best way to find out is to try.
Unfortunately you are right. If you run out of addresses (100 in the pool) Bitcoin-qt would have generated new addresses and those are not in that old backup, so you don't have the newly created private keys then you can't access the coins on them.
You better start using a deterministic wallet, like Electrum or Armory, if you don't have set up a good (automatic) backup process.