Although supertest is not that well documented, you can have a look into the tests/supertest.js.
There you have a test suite only for the query strings.
Something like:
request(app)
.get("https://stackoverflow.com/")
.query({ val: 'Test1' })
.expect(200, function(err, res) {
res.text.should.be.equal('Test1');
done();
});
Therefore:
.query({
key1: value1,
...
keyN: valueN
})
should work.