An LLC has to elect to be taxed as a corporation so an 1120 (or 1120S) can be filed.
LLCs can file Form 8832 to elect their business entity classification as a corporation.
For more information see http://www.irs.gov/Businesses/Small-Businesses-%26-Self-Employed/Limited-Liability-Company-(LLC)
"An LLC that does not want to accept its default federal tax classification, or that wishes to change its classification, uses Form 8832, Entity Classification Election, to elect how it will be classified for federal tax purposes. Generally, an election specifying an LLC's classification cannot take effect more than 75 days prior to the date the election is filed, nor can it take effect later than 12 months after the date the election is filed. An LLC may be eligible for late election relief in certain circumstances. See Form 8832 General Instructions for more information."
File Form 2553, Election by a Small Business Corporation, to elect classification as an S corporation. LLCs electing classification as an S corporation are not required to file Form 8832 to elect classification as a corporation before filing Form 2553.
See http://www.irs.gov/publications/p3402/ar02.html for more details.
You also asked "If I file a 1040 then doesn't that mean I can't take advantage of my LLC (C-Corp) status? Also, wouldn't an LLC allow me protection from lawsuits, bankruptcies, etc."
Although the LLC is disregarded for tax purposes the LLC can still allow protection from lawsuits, bankruptcies, etc. The LLC protects your assets as a corporate structure does and can mean that banks and other lenders cannot seize your personal property.
Please ask if you need more discussion or information.