I can give you the short answer on why DOITQ is relevant.
As Q put it: 1/billion chance.
Its probably a much bigger odd that the POTUS, who just happens to be working with Q - gets a randomized file name "DOITQ".
So LOGICAL THINKING says - what is more likely
a. The POTUS received a random file hash that just so happens to be popular phrase used by the mysterious anon and group who are secretly working for the POTUS?
b. Someone somewhere has the secret sauce to Twitters hashing algorithm and can use it to name files whatever they want.
so the logical answer is obviously b. which then leads us to who is doing this and why.
Q & POTUS need to be able to signal enough to anons to inspire belief but not enough to openly admit to the enemies who are also watching the boards that Q is really actually legit.
In July/August the strategy changed. Q said that the Q-anon project is a research project but also a public disclosure.
By being on these boards reading the breads you are participating in the full public disclosure. You are the "first responder" to a global catastrophe and you will be useful later by keeping the public calm during the transition through the use of the knowledge you have acquired here.
So yes, the Twitter POTUS file name is a "proof" but its designed to be ambigious enough to not give up the ghost of the whole op.
Be patient, Trust the Plane, Logical Thinking, Read Between the Lines
These are crucial while the project is still putting all assets into position for the big reveal.