\documentclass[beamer]{standalone}
\usepackage{tikz}
\usetikzlibrary{external}
\tikzexternalize % activate! 
\begin{document}
\begin{standaloneframe}

% If overlays do not work, use \only<1-n>{...} where n is the max overlay
 \only<1-2>{
  \begin{tikzpicture}[]
    \node (q) at (0,0) {\small$q$};
    \node (q0) at (-0.5,1) {\small$q_0$};
    \node<2-> (q00) at (-0.75,2) {\small$q_{00}$};
    \node<2-> (q01) at (-0.25,2) {\small$q_{01}$};
    \node (q1) at (0.5,1) {\small$q_1$};
    \node<2-> (q11) at (0.75,2) {\small$q_{11}$};
    \node<2-> (q10) at (0.25,2) {\small$q_{10}$};
    
    \draw (q0)  -- (q) -- (q1);
    \draw<2-> (q00)  -- (q0) -- (q01);
    \draw<2-> (q10)  -- (q1) -- (q11);
  \end{tikzpicture}
 }
\end{standaloneframe}
\end{document}