Overlay symbol with another

You can overlay the symbols the following way: Box the wider one and let the other one lap over it (using \rlap or \llap). The correct centering is achieved by placing the second character into a box with the equal width but using \hss to center it. The correct size for the different math modes can be adjusted using \mathchoice.

\documentclass{article}
\def\qeq{\mathrel{%
    \mathchoice{\QEQ}{\QEQ}{\scriptsize\QEQ}{\tiny\QEQ}%
}}
\def\QEQ{{%
    \setbox0\hbox{=}%
    \rlap{\hbox to \wd0{\hss?\hss}}\box0
}}

\textwidth=2cm
\begin{document}

$ A \qeq B $

$ A = B $

\[ A \qeq B \]
\[ A = B \]

$ S_{ A \qeq B } $

$ S_{ A = B } $

$ S_{S_{ A \qeq B }} $

$ S_{S_{ A = B }} $

\end{document}

Result

You could also use the Plain macro \ooalign:

$\mathrel{\ooalign{\hss?\hss\cr=}}$\bye

The just submitted stackengine package is tailor made for combining glyphs. Since it was just submitted to CTAN, it will hopefully propagate this weekend.

\documentclass{article}
\usepackage{stackengine}
\usepackage{graphicx}
\parskip 1ex\parindent 0in
\begin{document}
%Arguments to inset commands{overlay image}{base image}{V-offset}{H-offset}
Relative to bottom vs. top:\\
\bottominset{*}{O}{}{}%
\topinset{*}{O}{}{}%

With V and H shifting:\\
\topinset{*}{O}{}{}%
\topinset{*}{O}{1pt}{}%
\def\stackalignment{r}%
\topinset{*}{O}{2pt}{-1pt}%

Glyphs of different scales:\\
\def\stackalignment{c}%
\def\newi{\stackon[-.4ex]{i}{\scalebox{3}{.}}}
\def\useanchorwidth{T}
Th\newi s uses width of anchor alone

\def\useanchorwidth{F}
Th\newi s uses width of complete stack
\end{document}