You can, if you have two installations on your system at one time; one with CE 1.4 and one with CQM. (I'm doing it this way.
But you should definitely not
try to install CE and
CQM on the same installation. CE doesn't work with any mod that alters the game files, and you better believe that CQM alters a lot, lot, lot of them (and yes, it's vice versa - I'd bet that CQM doesn't like any mods that alter game files, too). The only things you can safely use with CE are reskins and such minor, graphical tweaks. Everything else and your game is prone to crash somewhere or misfunction horribly. Save yourself the stress and anger, don't try to mix one of the 'large' mods.
"... And the lord set a mark upon Caine lest any finding him should kill him and the mark was ..."