Stackelberg Oligopoly 3 firms
You are right that you first have to find F3's best-response function. F1 and F2 take as given this reaction of F3 to whatever they produce.
Hence, you plug this best-response function into the incumbents' profit maximization problem. In that way, you take care of the fact that the incumbents anticipate F3's reaction, indirectly determining $q_3$.

You should also check if the resulting reaction quantity $q_3$ is non-negative! It can be optimal to deter the entry of F3 completely.