Hjorimir
Adventurer
To quote Psion (I think): Rules serve the game, not vice-versa.
Given that it is a solo campaign I'd advocate doing what is fun for you and the player is a better choice than being too hung up on CRs. Just be mindful of the monster you are creating. A red dragon will add a lot of power to the character. Subsequently, it will be that much tougher to challenge the dragon without killing the PC outright. As long as you keep that in mind, do what is fun and fantastic and go with it!
Given that it is a solo campaign I'd advocate doing what is fun for you and the player is a better choice than being too hung up on CRs. Just be mindful of the monster you are creating. A red dragon will add a lot of power to the character. Subsequently, it will be that much tougher to challenge the dragon without killing the PC outright. As long as you keep that in mind, do what is fun and fantastic and go with it!