Lindsay, If I read your info correctly, you are currently licensed in another state and have knowledge of the industry, there are ways to do it pretty quickly. The issues become getting clearance through TREC and scheduling testing. The classes can be done in a months time. The scheduling and clearance can take another month depending on time of year and how busy they are....Welcome to Houston!
Lindsay, depending on the online school you choose, it could take as little as 4 weeks, i personally went to the classes to get the "extra" knowledge that is not in the material. Real Estate schools primary goal is to help you pass the State Exam, start looking at brokerages that train over ones that cost less. If you have any questions please let me know.
Depending on how dedicated your are, anywhere from three to nine months is the average. You might be able to do it faster, but I would not recommend doing it in less time than two to three months.