This question is hard to answer without more information, because how much income you report is going to depend on how the LLC is structured for accounting and tax purposes. If you haven't already consulted a CPA, I think finding one who has experience with LLCs would be a good idea - especially before you file taxes for 2011.
No matter what, the $6000 you've put into the LLC is an investment - it's your owner's equity. It's not a loan that the business pays back; you don't get the entire equity back unless you close the business or sell your share.
You take the LLC's gross income and subtract operating expenses to get net income or net loss for the LLC. The amount of net income is added to owner's equity on the books. The amount of net loss is subtracted from owner's equity.
The default for single-member LLCs is to be treated as a sole proprietorship for tax & accounting purposes. Any net income (or loss) for the LLC is reported on your 1040 & related schedules. Having net income on the books that you report does not mean you are getting any cash for personal use - you usually have to keep money invested while the business is growing.
After the business has been profitable, you can start taking withdrawals against your owner's equity. The money you take as a withdrawal lowers the total equity, but doesn't affect net income or loss for the LLC. Eventually you will probably build up enough equity to get back the $6000, but it can take awhile. I'm pretty sure that you personally wouldn't count any withdrawals on your initial investment as income, but that's something to look into.
There are options to set up the LLC as a corporation, which could be better for you as far as reporting income for taxes, but this requires more paperwork with the IRS and Washington State.
It's possible that there won't be any income from the LLC in 2012 - corporations regularly match expenses to income to avoid paying taxes, so I don't see why you can't take advantage of that. You also need to find out how often you are required to report any income - monthly, annually, etc.
The main factor, I think, is going to be whether you meet the minimum search requirements - be able to work, actively seek work, and available to start when you are offered suitable work.