Prepending digits to section numbers in ToC

I have more than ten sections that I want to list in the ToC as the following:

Which means I need to prepend 0s to sections of \ifnum\thesection<10. How do I do this in the ToC?

MWE :

\documentclass[10pt,a4paper]{article}
\usepackage{titlesec,titletoc}

\titleformat{\section}{\Large\bfseries}{
\ifnum\thesection<10 Q 0\thesection
\else Q \thesection \fi
}{0.5em}{}
\titlecontents{section}[0.5em]{}{
\large \textbf{Q\contentsmargin{20pt} \thecontentslabel\enspace} }
{\contentsmargin{20pt}\normalfont}{\titlerule*[1mm]{ $\cdot$}\contentspage}

\begin{document}
\tableofcontents
\section{}
% Returns "Q  1 ..." for ToC
% Returns "Q 01 ..." for Section Heading

\end{document}

• Quick and dirty: Edit the ToC-file. Jun 25 '19 at 18:24

This is my try by redefining \thesection:

\documentclass[10pt,a4paper]{article}
%\makeatletter
\renewcommand{\thesection}{\ifnum\value{section}<10 Q~{0\arabic{section}}\else Q~\arabic{section}\fi}
%\makeatother
\usepackage{titlesec,titletoc}

\titleformat{\section}{\Large\bfseries}{\thesection}{0.5em}{}

\begin{document}
\tableofcontents
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\section{}
\subsection{}
\subsection{}
\subsection{}

\end{document}