The Doctor presses a button marked RANDOM DESTINATION and exits the TARDIS to find himself on a ship. Not just any ship, the RMS Titanic.
He starts to get overwhelmed by all the memories of the past in such a young body, and nearly falls off the ship when a man rescues him just in time. The man introduces himself as Gerald, and is surprised when the Doctor introduces himself.
"How does a young person like you have a doctorate already?"
"Practice and declaration."
They hit it off well and Gerald invites the Doctor to have dinner with him. At the dinner, Doctor notices the iceberg going past the window. He can also feel the ship shaking slightly.
"Should we be worried about that?" Doctor asked, pointing out the iceberg going past the windows.
"Nah," Gerald responded, "what could that do? Provide us rocks for the bourbon?"
The ship starts sinking. In the ensuing chaos, Doctor loses sight of Gerald, and decides it's just better to leave and not mess with this point in time.
When he returns to the TARDIS, he senses a presence. A turn around reveals a Gerald in awe of what he was seeing.
Cue "It's bigger on the inside than it is on the outside!"
Cue an amused Doctor, and a briefing on what the hell is going on.
Cue the companion agreeing to travel with the Doctor.
Roll Credits - The Doctor Will Return in: Title Sequence
A/N: As you probably noticed, there is no title sequence. I'm stealing the whole "no title sequence in the first episode" from The Woman Who Fell to Earth.