Basically you can install a KDE app in Gnome and vice versa and Mint has no problems with that.
I don't know much about Quanta but the home page states
Quanta is based on KDE so this means it is network transparent from any dialog or project. It can use not only FTP but other KDE KIO slaves from file dialogs or in project settings.
I think this indicates a possible dependency problem in Gnome. You will have to install the proper KDE libs but when Quanta was installed that should have been done. Synaptic shows a few kde files to be installed
Don't fix it if it ain't broken, don't break it if you can't fix it