The way that I usually go about it is using a temporary table. It's probably not computationally efficient but it seems to work ok! Here i am duplicating record 99 in its entirety, creating record 100.
CREATE TEMPORARY TABLE tmp SELECT * FROM invoices WHERE id = 99;
UPDATE tmp SET id=100 WHERE id = 99;
INSERT INTO invoices SELECT * FROM tmp WHERE id = 100;
Hope that works ok for you!