It's one of baby Maxwell Drew's first outings, but Jessica Simpson made sure to keep her little one under wraps, while on a routine doctor visit with fiance Eric Johnson in LA, on Friday afternoon.

The proud new dad took the driver's seat, while Jess rode shotgun and her assistant sat in the back with the 2-week-old tot. Simpson recently signed an $800K deal with People mag for the first photos of her daughter, so she has to be extra careful not to reveal her baby's face before the mag comes out!

In addition to her huge photo deal, and the new launch of her own affordable maternity line, the Fashion Star mentor also reportedly has a $4 million contract to drop the baby weight with Weigh Watchers -- she's rumored to have gained over 40 lbs during her pregnancy.

Jess keeps rollin' in the dough!