How to make edges to the leaf nodes horizontal in a TikZ horizontal tree?

As you surmised, you're adding extra brackets which is making empty nodes, which doesn't work out of the box when the grow direction is horizontal (see Leaf nodes in tikz-qtree are not aligned with parents when using grow=left). This is due to how the anchor is set by default in tikz-qtree. I think the the best solution is not to use them at all. This obviously removes the horizontal edges entirely. I've also cleaned up your code substantially, making some styles for repeated things, and \node commands that aren't needed. If you have a lot of these trees to do, I would suggest switching to forest which uses the same basic input method (a labelled bracketing) but with a much more usable means for styling individual nodes and edges (no need for explicit \node or \edge commands).

\documentclass{article}
\usepackage{tikz,tikz-qtree}

\begin{document}
\begin{tikzpicture}[
            grow'=right,
            level distance = 2cm,
            level 2/.style={level distance=2cm,sibling distance=1cm},
            level 3+/.style={sibling distance=1cm},
            frontier/.style={distance from root=10cm},
            el/.style={sloped,font=\small},
            every leaf node/.style={font=\Large}
            ]
            \Tree 
            [.\node[draw,rectangle,minimum size=0.8cm]{1};
                \edge node[above,el]{Build A};
                [.\node[draw,circle]{2};
                    \edge node[above,el]{Good(0.6)};
                    [.\node[draw,circle]{4};
                         \edge node[above,el]{ Good(0.9)}; $\triangle$ 
                         \edge node[below,el]{ Bad(0.1)}; $\triangle$  
                    ]
                    \edge node[el,below]{Bad(0.4)};
                    [.\node[draw,circle]{5}; \edge node[above,el]{Bad(1)}; $\triangle$  ]
                ]
                \edge node[below,el]{Build B};
                [.\node[draw,circle]{3};
                    \edge node[above,el]{Good(0.6)};
                    [.\node[rectangle,draw,minimum size=0.8cm]{6};
                        \edge node[above,el]{ Expand};
                        [.\node[draw,circle]{8};
                             \edge node[above,el]{Good(0.9)}; $\triangle$ 
                             \edge node[below,el]{Bad(0.1)}; $\triangle$ 
                        ]
                        \edge node[above,el]{No Expand};
                        [.\node[draw,circle]{9};
                            \edge node[above,el]{Good(0.9)}; $\triangle$ 
                             \edge node[below,el]{Bad(0.1)}; $\triangle$  
                        ]
                    ]
                    \edge node[below,el]{Bad(0.4)};
                    [.\node[draw,circle]{7}; \edge node[above,el]{ Bad(1)}; $\triangle$ ]
                ]
            ]
        \end{tikzpicture}
\end{document}

If you do want the empty nodes, you can set the node anchors to center:

\documentclass{article}
\usepackage{tikz,tikz-qtree}

\begin{document}
\begin{tikzpicture}[
            grow'=right,
            every tree node/.style={anchor=center},
            level distance = 2cm,
            level 2/.style={level distance=2cm,sibling distance=1cm},
            level 3+/.style={sibling distance=1cm},
            frontier/.style={distance from root=10cm},
            el/.style={sloped,font=\small},
            every leaf node/.style={font=\Large},
                       ]
            \Tree 
            [.\node[draw,rectangle,minimum size=0.8cm]{1};
                \edge node[above,el]{Build A};
                [.\node[draw,circle]{2};
                    \edge node[above,el]{Good(0.6)};
                    [.\node[draw,circle]{4};
                        [ \edge node[above,el]{ Good(0.9)}; $\triangle$ ]
                        [ \edge node[below,el]{ Bad(0.1)}; $\triangle$  ]
                    ]
                    \edge node[el,below]{Bad(0.4)};
                    [.\node[draw,circle]{5}; \edge node[above,el]{Bad(1)}; $\triangle$  ]
                ]
                \edge node[below,el]{Build B};
                [.\node[draw,circle]{3};
                    \edge node[above,el]{Good(0.6)};
                    [.\node[rectangle,draw,minimum size=0.8cm]{6};
                        \edge node[above,el]{ Expand};
                        [.\node[draw,circle]{8};
                             [\edge node[above,el]{Good(0.9)}; $\triangle$ ]
                             [\edge node[below,el]{Bad(0.1)}; $\triangle$ ]
                        ]
                        \edge node[above,el]{No Expand};
                        [.\node[draw,circle]{9};
                            [\edge node[above,el]{Good(0.9)}; $\triangle$ ]
                            [ \edge node[below,el]{Bad(0.1)}; $\triangle$ ] 
                        ]
                    ]
                    \edge node[below,el]{Bad(0.4)};
                    [.\node[draw,circle]{7}; \edge node[above,el]{ Bad(1)}; $\triangle$ ]
                ]
            ]
        \end{tikzpicture}
\end{document}

Please see if it meets the requirement__ I have punched in only one label but it should suffice --the other labels follow the same syntax

\documentclass{article}
\usepackage{tikz,tikz-qtree}
\usetikzlibrary{shapes,trees}
 \begin{tikzpicture}[level distance=2cm,
        level 1/.style={sibling distance=7cm},
        level 2/.style={sibling distance=4cm},
        level 3/.style={sibling distance=2cm},
        grow'=right,
        ]
        \tikzstyle{every node}=[draw,
        circle,
        draw=red!50!black,thick,
        fill=green!30]
        \node (Root){1}
        child {node{2}
                 child {node{4} 
                    child{coordinate[]{}
                        child {node[xshift=2cm]{{\color{red}\Large $\triangle$}}}} 
                    child{coordinate[]{}
                        child{node[xshift=2cm]{{\color{red}\Large $\triangle$}}} }
                      }
                child {node{5} 
                    child{coordinate{}
                        child {node[xshift=2cm]{{\color{red}\Large $\triangle$}}}}
                            }
                        edge from parent  node [draw=none,fill=none,sloped,above] {\tiny Build A}
                }
        child {node{3}
            child {node{6} 
                child {node{8} 
                    child{coordinate[]{}
                        child {node{\color{red}\Large $\triangle$}}} 
                    child{coordinate[]{}
                        child{node{\color{red}\Large $\triangle$}}}}
                child {node{9} 
                child{coordinate[]{}
                    child{node{\color{red}\Large $\triangle$}}}}
            }
            child { node{7} 
                child{coordinate{}
                    child {node[xshift=2cm]{{\color{red}\Large $\triangle$}}}}
            }
        }
 ;        
 \end{tikzpicture}
\end{document}