How do I center this qtree?

The spacing in the tree is by design. The package tries to minimize the total width of the tree. If you centred node E, you would have to move F further to the right, making the whole tree bigger. Even if you make the nodes further apart with [sibling distance=30pt] (as an example) it will still give you an angled middle branch. This way the space between AA/CC is equivalent to the space between EEEEEE/GG.

If you truly want a vertical middle bar, you can manually adjust the node that is causing the problem (in this case the imbalance between CC and EEEEEE). But this will make the space between AA/CC and EEEEEE/GG no longer equal. So either way you end up with some asymmetry in the tree.

I also removed some unnecessary code from your example. The whole tree doesn't need to be in a \node and you don't need to load the tikzlibrary{trees} to use tikz-qtree (it uses low level pgf methods for tree construction.)

\documentclass[10pt]{article}
\usepackage{tikz}
\usepackage{tikz-qtree}

\begin{document}

\begin{tikzpicture}
% no adjustment
  \Tree 
 [.{ABC} 
    [.\textbf{D}
        [.AA BB ] ]
    [.\textbf{E}
        [.CC DD ]
        [.EEEEEE FF ] ]
    [.\textbf{F}
        [.GG HH ] ]
  ]

% Manually adjusted tree
\begin{scope}[xshift=3in]
\Tree 
 [.{ABC} 
    [.\textbf{D}
        [.AA BB ] ]
    [.\textbf{E}
        [.\node[minimum width=4.75em] {CC}; DD ]
        [.EEEEEE FF ] ]
    [.\textbf{F}
        [.GG HH ] ]
  ]
\end{scope}
\end{tikzpicture}

\end{document}

with automatic adjustment

\documentclass{article}
\usepackage{tikz-qtree}
\usepackage{calc}    
\begin{document}

\begin{tikzpicture}
  \Tree 
 [.{ABC} 
    [.\textbf{D}
        [.AA BB ] ]
    [.\textbf{E}
        [.\makebox[\widthof{EEEEEE}]{CC} DD ]
        [.EEEEEE FF ] ]
    [.\textbf{F}
        [.GG HH ] ]
  ]
\end{tikzpicture}

\end{document}