Is the steady state of $k$ enough to show $Y$ grows at the rate $n+g$?
Based on the steady state your production function is Cobb-Douglas.Taking logs and derivatives wrt time of $Y$, $\frac{Y}{L}$ and $\frac{Y}{AL}$ in the steady state yields the desired result: $K$ grows with $n+g$ on the BGP. 

It would be interesting to know what the supervisor's objection was.