I started a small online business this year and received a total income of $1,202.24. But I also know that Texas doesn't have income tax, so I don't know how to file this

[Texas Roger]

If you had more than $100 of expenses, you will have to upgrade to the online Self-Employed version or any one of the CD/download versions to get Schedule C to complete your tax return.

[Critter]

Texas doesn't but the feds do ...

If you have net self employment income of $400 or more you have to file a schedule C in your personal 1040 return for self employment business income. You may get a 1099-Misc for some of your income but you need to report all your income.  So you need to keep your own good records. Here is some reading material……

IRS information on Self Employment….
http://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Self-Employed-Individuals-Tax-Center 

Publication 334, Tax Guide for Small Business
http://www.irs.gov/pub/irs-pdf/p334.pdf 

Publication 535 Business Expenses
http://www.irs.gov/pub/irs-pdf/p535.pdf 

There is also QuickBooks Self Employment bundle you can check out which includes one Turbo Tax Home & Business return and will help you keep up in your bookkeeping all year along with calculating the estimated payments needed ....
http://quickbooks.intuit.com/self-employed