Smallest prime that is a quadratic residue modulo a fixed prime

Question

Let $P$ denote the set of positive primes and let $p$ be a fixed prime. Then define $q_{p} : = \min \{q \in P : p < q \; , (q/p) = 1 \}$ where $(\cdot / p)$ is the Legendre symbol. So for instance $q_{3} = 7$ and $q_{5} = 11$. Is there anything known about $q_{p}$ and specifically are there known bounds on $q_{p}$ as a function of $p$? I am ultimately interested in investigating $\inf \{q_{p}/p : p \in P \}$.