maybe try just adding a hidden form element to pass the page parameter:
<form action="index.php" method="get" id="clientSearchForm" name="clientSearchForm">
Employer Name:
<input type="hidden" name="page" value="empquicksearch" />
<input type="text" name="empSearchName" id="empSearchName" />
<input type="submit" name="empSearchButton" id="empSearchButton" value="Submit" class="submit" />
</form>