They call this a parody. It's really more of an ode in my opinion. This brilliant production by the Hillywood Show pairs Doctor Who with the "Time Warp" from the Rocky Horror Picture Show. It stars Hilly Hindi as the tenth Doctor, and while she does a great job, particular accolades must go to Elliot "Ell Shmell" Crossley, who does the Doctor's voice. It's an uncanny impersonation of David Tennant's voice. Have a watch!
In other news, the first teaser trailer for the new series of Doctor Who (which starts in August) was released a few days ago. It truly fits the word "teaser" as there's really nothing much to it. Compared to the above, it's an anti-climax, but here it is anyway.
And for a much better trailer, here's a fan-made one from the same person responsible for "Wholock" and "Stone".