Edit in JSFiddle

function CheckForOther(item, origlen) {
    var sitem = item.options[item.selectedIndex];

    if (item.selectedIndex == (item.length - 1)) {
        var val = prompt("ADD A NEW CHOICE:", "");

        if (val === null) item.selectedIndex = 0;
        else {
            var slen = item.length;

            if (slen == origlen + 1) {
                item.options[slen] = new Option(sitem.text, sitem.value);
            }

            item.options[item.length - 2].text = val;
            item.options[item.length - 2].value = val;
            item.selectedIndex = item.length - 2;
        }
    }
}

function validateForm(theForm) {
}

<h2>All Customers: Web Inquiries</h2>

<form name=qdbform method=POST onsubmit='return validateForm(this)' encType='multipart/form-data' action=https://www.quickbase.com/db/bj3vc3z73?act=API_AddRecord&apptoken=cwfcy7gdzqrsyncqbi2bn4u4kr>
    <input type=hidden name=fform value=1>
    <table>
        <tr>
            <td class=m>Name:</td>
            <td class=m>
                <input type=text size=40 name=_fid_6>
            </td>
        </tr>
        <tr>
            <td class=m>Company:</td>
            <td class=m>
                <input type=text size=40 name=_fid_7>
            </td>
        </tr>
        <tr>
            <td class=m>Email:</td>
            <td class=m>
                <input type=text size=40 name=_fid_8>
            </td>
        </tr>
        <tr>
            <td class=m>Phone:</td>
            <td class=m>
                <input type=text size=40 name=_fid_9>
            </td>
        </tr>
        <tr>
            <td class=m>Suburb:</td>
            <td class=m>
                <input type=text size=40 name=_fid_11>
            </td>
        </tr>
        <tr>
            <td class=m>State:</td>
            <td class=m>
                <select onChange=CheckForOther(this,5) name=_fid_12>
                    <option>QLD</option>
                    <option>VIC</option>
                    <option>NSW</option>
                    <option>WA</option>
                    <option>&lt;Add New Choice...&gt;</option>
                </select>
            </td>
        </tr>
        <tr>
            <td class=m>Inquiry Type:</td>
            <td class=m>
                <select onChange=CheckForOther(this,4) name=_fid_13>
                    <option>Sales</option>
                    <option>Service</option>
                    <option>Tech Support</option>
                    <option>&lt;Add New Choice...&gt;</option>
                </select>
            </td>
        </tr>
        <tr>
            <td class=m>Product Interested In:</td>
            <td class=m>
                <input type=text size=60 name=_fid_14>
            </td>
        </tr>
        <tr>
            <td class=m>Message:</td>
            <td class=m>
                <textarea name=_fid_10 rows=6 cols=60></textarea>
            </td>
        </tr>
    </table>
    <input type=hidden name=rdr value='http://www.countrysolar.com.au/contact/thank-you'>
    <input type=submit value=Save>
</form>
<br />Powered by QuickBase <a href="http://quickbase.intuit.com/">Online Database</a>