This is not canon, I've never seen the original seasons so I couldn't really incorporate that into this but I hope you still like this.
"Still not ginger, I'm never ginger!" He cried, pulling at his hair in desperation, grinning madly at the blonde girl before him. Rolling her eyes, she turned away as a smile graced her lips, missing the sorrow in the tall, lanky man's eyes.
Kissing the forehead of her son, the redheaded women linked her hands with his. Together they ventured into the city, the small boy gazing around in wonder at the dazzling buildings that reached for the heavens. The red-orange sky made the city glow gold, a magnificent color. Beyond the walls stretched seas of red grass that smelled of honeysuckle, high mountains that sang in the wind and the ever-present hum of time that cloaked the planet.
It was today that he would start his first day of school, leaving behind the friendliness of his happy household and thrust into the world. To his dismay, he was the only ginger in his class, and at first the other children giggled at the shocking color. Smooth tones of Galiphreyan filled with years of knowledge and wisdom wound around him and he soaked it in, not letting a single ounce of it escape him.
Some days they were aloud to run, and oh he loved to run. Dashing through the scarlet grasses, letting their sweet aroma engulf him as he sang in the melodies of a time lord. Every passing second felt like heaven to him, the beauty of his planet never tiring.
To his father he was a disappointment, someone more interested in daydreaming then one of the righteous jobs that were given only to the best. Oh he had the smarts; his brain was always whirring away a thousand miles a minute, but power and ruling held no interest for him. Once completing his studies he would slip away to the Mountains of Solace and Solitude just to think. He let his mind wander to the far edges of the galaxy, dreaming of the places he could go and the people he could see. The opportunities were endless and he was dying to get away.
He wanted a T.A.R.D.I.S more then anything. With one of those he could travel the stars, see anything and everything he wanted.
But only the high authorities got those.
As he grew older the city grew darker, more whispers behind closed doors and less cheerful smiles in the streets. It troubled him that time no longer seemed to flow as strongly through their veins, something was blocking it and it unnerved him. His friends talked of war but still his mother would reach to ruffle his rust-hair, kiss his cheek and tell him not to worry, it was all under control. (He knew it wasn't)
They started recruiting people for war and that's when he knew he had to get out. He'd had his eye on a TARDIS, one he knew no one would miss. It was in a museum, nearly 40 years past it's prime, nobody would even notice it was gone. He slipped inside when the lights went out (it was a bit surprising since everyone said it never opened for anyone)
And the ship was more beautiful then anything he'd ever seen.
He somehow managed not to kill himself on the first run, (and he wasn't sure if he'd imagined it but he thought that maybe the ship was laughing at him) He wasn't sure how long he'd traveled, time sort of blended together but never once did he think about going back.
But the TARDIS had a mind of her own and even though he didn't want to he found himself back at Gallifrey just in time to kill everyone he loved. He watched as his magnificent planet burned, he swore he could hear their screams in his head. Fire; there was so much fire stretching across the seas of scarlet grass and the looming mountains.
He locked away the nightmares, shoved the screams and the pain to the utmost corners of his mind but every time he looked in the mirror and saw his bright hair he felt a certain tug at his heart, a tug for parents and siblings and even the friends that had mocked him. He missed them.
He was lonely.
But then he regenerated, he knew it would happen eventually but he hadn't been expecting this. He thought he had more time.
He hesitated before he looked in the mirror, and nearly cried out when he saw what he had become. His hair-his ginger hair- it was gone. Replaced with brown, boring, boring brown. It was always brown, sometimes blonde but rarely. All he wanted was his red hair, his wonderfully beautiful red hair. Sometimes his companions had red hair, he was jealous of them oh so jealous because he could never seem to get his back.
Rose didn't see the flicker of sadness in her Doctor's eyes, didn't see how he ruffled his hair gently, maybe hoping if he looked again it would have changed. But it didn't, it never did.