The following is some friendly, non-legal advice based other homeschooler’s experiences.
Yes. Homeschooling is legal in Texas. You are considered a private school in Texas. And in Texas, of course, private schools are unregulated. This means that public school officials can not request to review or approve your curriculum. The Texas education code describes the exemption from compulsory school attendance as follows:
Title 2. Public Education; Subtitle E. Students and Parents; Chapter 25. Admission, Transfer, and Attendance Subchapter 25. Admission and Enrollment 25.086. Exemptions
(a) A child is exempt from the requirements of compulsory school attendance if the child: (1) attends a private or parochial school that includes in its course a study of good citizenship;
Also note the following part of the exemption:
(b) This section does not relieve a school district in which a child eligible to participate in the district's special education program resides of its fiscal and administrative responsibilities under Subchapter A, Chapter 29, or of its responsibility to provide a free appropriate public education to a child with a disability.