Are you planning to visit mid or is mid planning to visit you? If the latter, you must take into account that your mid might not be able to leave for some or all of the T-giving leave period. Reasons that mids end up voluntarily or involuntarily staying over Thanksgiving include: duty/watch, academic issues, fitness issues, conduct issues, varsity sports, band practice, etc.
I understand the temptation to book now but remember that your child is in the military. Things can -- and do -- change in ways that are not "fair." The fact that someone will lose a lot of money on an airline ticket is not a persuasive argument in military life. Thus, if you book now, just be prepared to pay the hefty change/cancellation fees if something unexpected occurs.