AJAX building query string from checkbox array

Hi all,

I'm trying to build a querystring from a check box array.

Here's my AJAX code - the var options and var querystring are the areas I'm guessing I need to flesh out but not quite sure how to do it:

<script language="javascript" type="text/javascript">
<!-- 
//Browser Support Code
function ajaxFunction(){
	var ajaxRequest;  // The variable that makes Ajax possible!
	
	try{
		// Opera 8.0+, Firefox, Safari
		ajaxRequest = new XMLHttpRequest();
	} catch (e){
		// Internet Explorer Browsers
		try{
			ajaxRequest = new ActiveXObject("Msxml2.XMLHTTP");
		} catch (e) {
			try{
				ajaxRequest = new ActiveXObject("Microsoft.XMLHTTP");
			} catch (e){
				// Something went wrong
				alert("Your browser broke!");
				return false;
			}
		}
	}
	// Create a function that will receive data sent from the server
	ajaxRequest.onreadystatechange = function(){
			if(ajaxRequest.readyState == 4){
			document.getElementById('result').innerHTML = ajaxRequest.responseText;
		}
	}
	//Need to grab query string and append checked checkboxes array
	var options = document.get......
	var queryString = "?filter_options=" + options....;
	ajaxRequest.open("GET", "filter_query.php" + queryString, true);
	ajaxRequest.send(null);  
}

//-->
</script>

Select allOpen in new window

Here's some checkboxes:

<label for="1"><input type="checkbox" onClick="ajaxFunction();" name="filter_option[]" value="1" id="1">Option 1</label>
<label for="2"><input type="checkbox" onClick="ajaxFunction();" name="filter_option[]" value="2" id="2">Option 2</label>
<label for="3"><input type="checkbox" onClick="ajaxFunction();" name="filter_option[]" value="3" id="3">Option 3</label>

Select allOpen in new window

There can be loads of these and I was thinking of sending the string of id's to the server like:
filter_option=1-2-3-4-5-45-34-67-89 and doing an explode() on them before querying.

Lastly, the user arrives at this page with variables in the URL obtained via GET already.

e.g. search.php?qs=My+Search&date=3m


So I have a few questions around this:
A) How can this be achieved?
B) Is this the best way and is this fully browser compliant?
C) How can I include the variables already in the URL in the AJAX call? Write them into it via php?

Huge thanks
David