You can typeset a harpoon, back space and typeset another one:
\documentclass{article}
\usepackage{amsmath}
\newcommand{\paronto}{%
\rightharpoonup\mathrel{\mspace{-15mu}}\rightharpoonup
}
\begin{document}
$f\colon X\paronto Q$
\end{document}

With the help of trimclip you can make the symbol to have the same dimension as the single headed arrow:
\documentclass{article}
\usepackage{amsmath}
\usepackage{trimclip}
\DeclareRobustCommand{\paronto}{%
\clippedrightharpoonup\mathrel{\mspace{-15mu}}\rightharpoonup
}
\makeatletter
\newcommand{\clippedrightharpoonup}{%
\mathrel{\mathpalette\clipped@rightharpoonup\relax}%
}
\newcommand{\clipped@rightharpoonup}[2]{%
\sbox\z@{$\m@th#1\mspace{3mu}$}%
\smash{\clipbox{{\wd\z@} 0pt 0pt {-\width}}{$\m@th#1\rightharpoonup$}}%
}
\makeatother
\begin{document}
$f\colon X\paronto Q_{\paronto}$
$f\colon X\rightharpoonup Q_{\rightharpoonup}$
\end{document}

With a rounded stem:
\documentclass{article}
\usepackage{amsmath}
\usepackage{trimclip}
\DeclareRobustCommand{\paronto}{%
\clippedrightharpoonup\mathrel{\mspace{-15mu}}\rightharpoonup
}
\makeatletter
\newcommand{\clippedrightharpoonup}{%
\mathrel{\mathpalette\clipped@rightharpoonup\relax}%
}
\newcommand{\clipped@rightharpoonup}[2]{%
\sbox\z@{$\m@th#1\mspace{6mu}$}%
\clipbox{0pt 0pt {\dimexpr\width-.5\wd\z@} 0pt}{$\m@th#1\rightharpoonup$}%
\smash{\clipbox{{\wd\z@} 0pt 0pt {-\width}}{$\m@th#1\rightharpoonup$}}%
}
\makeatother
\begin{document}
$f\colon X\paronto Q_{\paronto}$
$f\colon X\rightharpoonup Q_{\rightharpoonup}$
\end{document}
