//store the paths you iterate
std::vector<QString> paths;
paths.emplace_back("first path");
paths.emplace_back("second path");
if(input_path == "cd"){
    QDir new_path(paths.back());
    new_path.cd();
    paths.emplace_back(new_path.absolutePath());
}

//back to previous path, stl split back and pop_back to two actions for the sake of exception safe
auto const path = paths.back();
paths.pop_back();