Duff and her husband Mike Comrie welcomed their first child Luca Cruz last month.
She has now told People that she is thrilled with everything her son does.
"The day is exciting if he makes a new face or he gets to take a real bath instead of a sponge bath," she said. "You know what was a big milestone? The belly button falling off. That was a huge one."
Duff continued: "I wanted to keep it but my husband was like, 'No, that's gross, you can't keep it!' I'm like, 'I'm totally keeping it' and I secretly kept it... But it's not a secret anymore. It's in a Ziploc bag in the back of my makeup drawer. Luca's going to think I'm a freak!"
Duff, who recently described motherhood as "joyful", also revealed that she loves breastfeeding her son.
"It's such a wonderful bonding time," she said. "Just to have your baby thrive and knowing that you're doing that and you're responsible - it's such a rewarding feeling."
Duff has said that motherhood has taught her to "let go" of how she does things.
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