0.00001 isn't worth worrying about but it just feels wrong to destroy them. I'd rather give them to a miner.
Are these bitcoins unspendable? How do I spend and/or give them away?
You can send a transaction without fees so long as:
* all the outputs (including change, if any) are 0.01 BTC or more
* the transaction is 10,000 bytes or smaller
* the priority is high enough
I'll address the 3 points in order:
* The first thing you're going to need to do is to get some more coins in your wallet, or you'll not be able to afford the fees (free to those that can afford it, very expensive to those that can't). Let's suppose you add 11 bitcoins.
* To keep the transaction size down, we'll send to a single output to ourselves. That
leaves you room for 55 inputs. One of the inputs is going to have to be the 11 bitcoins, leaving room for 54 satoshis of dust.
* Priority is determined by multiplying the age of each input by its size and summing the results then dividing by the transaction size in bytes. In order for the transaction to be free, the average age * size needs to be around 1 BTC day. Since the dust is never going to be old enough to contribute significantly to the priority, the 11 bitcoins is going to have to contribute enough to bring the average up. In order to spend 11 bitcoins on their own without a fee, the 11 bitcoins should be around 1/11 of a day old. We need them to be 55 times older than that to be spendable without a fee - so 55/11 = 5 days old.
So in summary, you can spend 54 satoshis at a time so long as you combine them with a 11 BTC coin that hasn't moved for at least 5 days.
You can then repeat the process every 5 days, adding about 54 satoshis of dust to the amount you transfer to yourself. Since you have 1000 satoshis to transfer, this is going to take quite a long time. Like 19 sets of 5 days, or 95 days. You could speed the process up if you can put more than 11 BTC into the wallet. The more value you can spend each time, the faster the priority goes up, and the less time you have to wait between transactions. If you can add 110 BTC instead of 11 BTC then the wait time goes down from 5 days to 0.5 days between transactions.
Note: I've not tried this to see if it really works, but what I've written is pretty close to how the satoshi client works in terms of deciding which transations need a fee.
Or you could just forget about it.