One simple solution I would suggest is to change the select as mentioned below
<select id="months">
<option value="1">January</option>
<option value="2">February</option>
<option value="3">March</option>
<option value="4">April</option>
<option value="5">May</option>
<option value="6">June</option>
<option value="7">July</option>
<option value="8">August</option>
<option value="9">September</option>
<option value="10">October</option>
<option value="11">November</option>
<option value="12">December</option>
<option selected="selected">Month</option>
</select>
because when appending the last option is getting selected by jQuery.
EDIT:
Change your else statement as below
else {
selectListOptions.appendTo(selectList);
$('#months option:contains("Month")').prop('selected', true);
}