What age is it safe to start working on vocal range?

Ok so I'm a 13 yr old male singer, been singing for a while now, and I have a bit of an issue. So my vocal range is g2 to f4 (G5 falsetto), which is clearly baritone range, right? But my problem is that I have a more tenor-like timbre, and I have an extremely young look. Now the reason this is a problem is because I'm very much into musical theatre, where I look and sound far too young to play most baritones, as they are commonly older men. The question isn't necessarily. So I was was wondering what a safe age might be to start working on vocal range, because my singing teacher advised not to, as he reckons it might cause more harm than good long term. He didn't mention what age I should start working on it, so I was wondering if people on here could tell me the answer?