When i read your question i assumed you would have dialogs open at the same time. hence signal would be the best. But it more like in sequence i see

it could be a bit cleaner if you can let mainwindow handle it and we then get rid of "one dialog open the other one" as its best to avoid if possible.
Its not wrong as such but not optimal as Qt::WA_DeleteOnClose can crash the
code.

what about something like ?

void mainwindow::Search() {
  SeachDia SD;
  InformationDialog infoDialog () ;
  if ( SD.exec() == Accepted) {
    Information* info = SD.retrieveInfo();
    infoDialog.setSearchData(info);
    infoDialog.exec();
  }
}

Also, it the order of

emit on_Info_Changed(Information);
infoDialog.exec();

correct?

close

Perhaps because the first dialog is closed but not deleted from memory?
You could set the Qt::WA_DeleteOnClose flag and see if it still works.

        close();
        Information* info = retrieveInfo();
        InformationDialog infoDialog;
        infoDialog.setModal(true);
        connect(this, SIGNAL(InfoChanged(Information*)), &infoDialog, SLOT(on_Info_Changed(Information*)));
        emit on_Info_Changed(Information);
        infoDialog.exec();

basically I want the first dialog to search for information and then close and display the information on the 2nd dialog. The above code works but I just don't get how "this" in connect() still exists after the call to close();

Will this code cause problems?

So you simple define a set of signals and slot that defines what they want to "say" to each other
and then hook it up.