It's stunning that you give more credence to your "hypothetical" Q document than you do for the actual, traditional Gospels that are well attested to by the early church fathers.
Q is a myth. It's anything you guys want it to be. How long is it? How many chapters? How many verses? Who wrote it (no clue there either). And zero manuscript evidence.
Here's what you need to know about Q:
Fallacies at the Heart of Q:
The Case Against Q: Fallacies at the Heart of Q
Ten Reasons to Question Q:
The Case Against Q: Ten Reasons
There's simpler explanations than having to posit the mythical Q. One of the big ones is that Matthew and Peter and John most likely sat around campfires after Jesus' resurrection and recalled what Jesus said and did. And according to Acts 1:3 Jesus spent forty days with them, no doubt recalling for them the numerous teachings and acts of his ministry. They may have even taken notes of some kind to be used later in their separate Gospels. But even that isn't necessary.
John 14 John clearly cites the Holy Spirit as helping him recall what Jesus taught. He's the PRIMARY source. Q is not necessary.
John 14:26 - "But the Advocate, the Holy Spirit, whom the Father will send in my name,
will teach you all things and will remind you of everything I have said to you."
That's the source skeptics ALWAYS sweep under the rug because they can't stand to admit the supernatural.
Just the opposite. There's actual compelling evidence for the traditional Gospel authors. See Post # 202:
Was Jesus Only Human?
There's ZERO manuscript evidence for your Q, and yet you believe. That requires a much greater faith than believing in the Lord Jesus Christ.