Check your eligibility. Some of them have restrictions based on citizenship, race, gender, or other characteristics. Notify your supervising professor that you are thinking about a dissertation grant. Government agencies usually require that the supervisor be the formal Principal Investigator. Follow the directions exactly.
Deadlines are important and real.
Besides the deadline published by the agency, UT requirements may take time to complete. Plan on completing the text of your proposal at least two weeks before it is due. Your ideas are more important than the literature review. Although it is important for readers to feel confident of your knowledge of the field, a dissertation grant proposal is not principally about your assessment of your field. It is about the contribution you will make to the field.