Avril Lavigne and Nickelback frontman Chad Kroeger's relationship has been so quiet that few even knew they were dating. Now, after a six-month courtship, the Canadian rockers are engaged to be married, Lavigne's rep tells PEOPLE exclusively. Lavigne, 27, and Kroeger, 37, first got together in February to co-write a song for Lavigne's upcoming fifth studio album. "A romantic relationship blossomed as they spent time writing together," a Lavigne pal tells PEOPLE. On Aug. 8, Kroeger popped the question, presenting Lavigne with a 14-carat diamond sparkler. "He makes her so happy," a family source tells PEOPLE. "Both of their families could not be more excited."