"As a matter of fact, if a dog climbs up in my lap, I feel like he gets a little jealous," she added when asked if Isaiah wants a little brother or sister.
Underwood married Fisher, an NHL player for the Nashville Predators, in 2010, and gave birth to Isaiah in February 2015.
She said in the November issue of Redbook that she savors quiet moments with her son.
"He'll be watching cartoons and I'll be watching him," the star shared. "I'm completely in love. I love it when he's sleepy and I get to hold him and smell him. He doesn't know I'm staring at him and being all googly-eyed!"
Underwood released her fifth studio album, Storyteller, in 2015, which includes the singles "Church Bells" and "Dirty Laundry."
She told "ET" she's already started work on her next album.
"The creative process is an interesting thing," the singer said.
"You never know when it's all just going to come together and then you'll finally be able to be like, 'I'm done! Wow, we've made an album.' So I'm kind of at the beginning stages of that, which is really fun."
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