You can copy the private key over from your existing wallet.
Your wallet.dat file can be on multiple clients at once.
BIG WARNING: The network will think you're trying to scam it by doing a double-spend if you send BTC from more than one client at a time. So if you're still just downloading the blockchain in Bitcoin-Qt just make sure to
not send anything using Bitcoin-Qt. If you've already sent something in Bitcoin-Qt, you need to wait for it to show up in all your clients or you can only use Bitcoin-Qt to send more coins. Basically, pick a client and stick with it.
I'll post instructions for copying the private key to Electrum. If you want the multibit instructions they are similar.
1. Install
Electrum - follow instructions at that link
2. When you first start it, it asks if you want to create a new wallet. Create a new wallet and write down the seed it gives you, then put that in a safe place. (This is all just the standard process for getting Electrum up and running.)
3. In Bitcoin-Qt, open the Help menu > click "Debug Window"
4. At the top of the Debug Window, click on the "Console" tab. It should show you "Welcome to the Bitcoin RPC console. Use up and down arrows..."
5. Type "listaddressgroupings" in the text box at the bottom
6. It will show you a list of all your addresses. Here's an example:
[
[
[
"1GiN4UWo8VZ9PZuJXfMQYbQyP9opGsayYD",
0.00000000,
"my wallet 1"
],
[
"1GiN4UWo8VZ9PZuJXfMQYbQyP9opGsayYD",
0.00000000,
"my wallet 2"
]
]
]
7. Pick the top address, so you're looking for something like 1GiN4UWo8VZ9PZuJXfMQYbQyP9opGsayYD
but that is my address. You want to get one of your addresses, then type "dumpprivkey 1GiN4UWo8VZ9PZuJXfMQYbQyP9opGsayYD" in the text box at the bottom. (Replace my address with your address when you type it.) If you want, you can use Copy (Ctrl-C) and Paste (Ctrl-V) to speed this up. If you type the address wrong (or paste it wrong) you'll get an error "Invalid Bitcoin address" or another error. Try typing again.
8. Do
not post the information it just gave you - that is the private key to that address, and it has the power to spend coins. Keep it safe!
9. Hilight that information it just gave you, and hit Ctrl-C to copy it.
10. Open Electrum and click the Wrench/Screwdriver icon at the bottom (Preferences)
11. In the Electrum Settings window, click the Import/Export tab
12. The third row is "Private Key" and has a button "Import" - click the "Import" button on the third row. I think Electrum shows a warning the first time, asking if you are sure you want to do this - click Yes.
13. paste the information from Bitcoin-Qt into Electrum and click OK
14. if you copy/pasted it correctly, Electrum then shows a Popup that just shows the address. This confirms you pasted it correctly. If it says something like "invalid password" go back and copy the information again from step 9
15. Click OK to clear the address popup. Click OK to close the Electrum Settings.
16. You can verify the address can now be used in Electrum by going to the Receive tab in the main window. If you see the address there, Electrum now knows about it and can send/receive the coins at that address.
17. Now that you've imported one address, you can go back to step 7 and get another address from Bitcoin-Qt
