In the Past classes have been dismissed at 12:30 pm the Wed. before Thanksgiving. Last year, the Mids leave expired at 1800 Sunday. The Academy (I believe Requires) that you are scheduled to arrive 4 hours prior to leave expiring.
Until it is actually shown on the USNA Calendar you do run the risk of things changing and you having to pay $$$ to change an airline ticket purchased this early.
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.
As stated above, our Mids are now part of the military. We learned really quickly last year with our daughter at NAPS that it was much easier for her to schedule her flights home as she knew what her schedule specifics were. We did watch the pricing and if I saw a variety of flights that might be of interest and at a decent price, I would copy that information and put it to her in an email. It became her "job" to secure the transportation that best fit the needs of the situation.
She always made sure to include a copy of the confirmation of her booking to my email address so that she had someone to pick her up at the airport.