What is the unit speed version of this curve?

Question

I'm trying to find the unit speed version of the curve $\gamma = (t, 0 , t^2)$. So far I have that $|\gamma^{\prime}|=(\sqrt{1+4t^2})$. I am not sure where to go from here though. My idea was to replace $t$ in $\gamma$ by $\frac{2}{(\sqrt{1+4t^2})}$, but since $|\gamma^{\prime}|$ didn't yield a constant, I'm not sure if this is the right way to go about this. I considered parameterization by arclength, but this doesn't seem like the right manner to go about this either.