In the caption accompanying the picture, she wrote: "Just taking a walk around the block... Street legal???"
Simpson, who is engaged to Maxwell's father Eric Johnson, has also recently tweeted about enjoying motherhood.
"I absolutely LOVE my family!" she said. "Maxwell amazes Eric and I every day with every little thing she does!"
Last month, Simpson became a spokesperson for Weight Watchers, though she has vowed to lose her baby weight responsibly.
Simpson, who has previously described motherhood as the "best thing" she has ever experienced, is also reportedly planning to launch a line of maternity clothing.
Meanwhile, her sister Ashlee Simpson recently described her as a "great" mother, saying that she is "so proud" of her.