var credentials = {
    username: 'bunnyman',
    password: '*******'
};

// Stuff the cookie into a global (for now)
var cookie;

request.post({
        uri: the_uri_of_the_login_api,
        headers: { 'content-type': 'application/json' },
        json: credentials
    }, function(err, res, body){
        if(err) {
            console.log("error", body);
        } else {
            cookie = body;
        }
    });

var query = {
    "input": { "some_form_property": "value" },
    "additionalInput": {
        "8d817939-your-api-key-f5dc9502ed72": cookie
    },
    "returnPaginationSuggestions": true
}
request.post({
    uri:  the_uri_of_the_query_api,
    headers: { 'content-type': 'application/json' },
    json: query
}, function (error, response, payload){
    if (error){
        console.log(payload);
    } else {
        console.log(payload);
    }
});