The client is downloading and verifying blocks from way back when the network first went up to this day, so until it reaches the block your transaction was in, it can't know about it. If you are in a hurry, you might want to use a light wallet such as Electrum.
No, but you can export the private key from the console (Help -> Debug window -> Console). Lets assume your password is 'passw0rd', so you enter:
which unlocks your wallet for 180 seconds.
With
you expose your private key. Make sure no one else sees it. Dont store it in the cloud, dont send it by mail. If you have to transfer it to a different machine use an USB stick.
Now (I assume you have your new electrum wallet open on the same machine here) switch to electrum and:
#1 Make sure you have a backup of the seed.
#2 Make sure you have a backup of the seed. Yes, I just wrote that, but you wouldnt believe how many bitcoins have already been lost because people have no backup of their seed. Make. a. backup. now.
#3 go to Wallet -> Private keys -> sweep, copy the private key into the box and click sweep.