It seems that QCE and Notepad++ interpret the multiline mode differently. Notepad++ is applying by default the "multiline" mode to all searches. In QCE, multiline regex mode is not active by default. To enable it, you have to prefix your "search what" with "m)" flag. For example:
search: m)$
replace: 1
The syntax to enable multiline search varies depending on the Regex implementations. The QCE regex syntax follows the AutoHotkey RegEx syntax.
More info here.
QCE could enable multiline mode by default but this would prevent doing non-multiline regex searches. Your opinion on this is welcome.