Heya, Scot! Casanova here to do a review for you!
*reads through till I see Matt*
Anyway, I'll be taking this verse by verse, so I hope you don't mind. To the review!
I've got a new face today,
Sent down from the Time Lords of Gallifrey.
I've got a whole new twelve life set,
More than any Time Lord should get.
You start off with a strong flow and a not too bad rhyme scheme, so I'll have to give you props for that. Anyway, onward!
I chased all the monsters away
On an eternal Christmas Day,
A town where no one lies,
On the planet where I was supposed to die.
I don't know much about Doctor Who, but this just seems a bit rushed to me. You go from chasing monsters away to supposed to have died. I didn't like the switch, in all honesty. I would like to have heard some about the journey in between, if you know what I mean. Anyway, onward.
I've broken science!
Gone against how the world's supposed to be.
Today I won't be dying.
Christmas is protected cause it's got me!
Here I got a little confused. I'm a lyricist as well, and one thing I know is rhyme schemes(rap is my thing, yo) and here your rhyme scheme changes, and I was wondering why that was? Your lines don't have to rhyme in order to be lyrics, but you should try to keep the rhyme scheme consistent. Anyway, onward.
The Doctor's face changes constantly.
Hartnell, Troughton, Pertwee,
That makes three.
Baker, Davison and Baker again!
The Doctor will never end.
McCoy, McGann ... wait ...
Admittedly ... he took a little break ...
And then came the reboot that
introduced us all to Chris, David ... Matt.
You have a AAA BB CC rhyme here. Instead of AABBCC- which I think would make it sound better. Again, this is different from the first rhyme scheme and the second rhyme scheme, and I thought that was odd. Anyway, onward.
And now look, see me?
I'm Peter Capaldi,
The face that can't possibly be ....
.
I've broken science!
Gone against how the world's supposed to be.
I'm never really dying.
The universe will always, forever and ever and ever and ever ... be protected ... because it's. Got. ME!
Here it seems like you're just messing around and having fun with the lyrics- which is always a good thing! I have nothing against writing something just for fun, and I would love to hear how this is supposed to go.
Overall, I think you have a decent idea with some rhyme issues and some minor flow problems. Beyond that I really can't review- considering I don't know much about doctor who at all. So props for the lyrics, it's always refreshing to read them.
Anyway, that's all I have to say on this one and I hope it helped.
Keep on doing what you're doing and keep on keeping on.
Your friend, Matt
And yes fanmusic is definitely a thing! In fact, when it's about Doctor Who, it's called Trock (Timelord Rock). The pioneering band of the genre is Chameleon Circuit and they are awesome. Anyway, thankyou 
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