Producer Timbaland is engaged to his girlfriend and publicist, Monique Idlett – and the pair have just welcomed a baby girl, a source close to the rapper tells PEOPLE.

Idlett, 33, gave birth to their daughter just a couple of days ago, according to the source.

Timbaland and Idlett have been dating for two years, and "they're both really happy together," says the source. "They've known each other for years."

The music producer (and pal of Justin Timberlake) proposed at the couple's baby shower in October.

This will be the first marriage for both; Timbaland and Idlett plan to tie the knot within the next year.