"In the UK, it's such a big thing to breastfeed in public and here it just seems to be so much more accepted," she says. "I think generally it's just a better place to be with a baby."
During their last trip, they rented a small home base, but travelled extensively around the country with visitors from abroad.
This time around, the family will be spending more time close to Auckland and they plan to explore the islands of the Hauraki Gulf.
While Mr Bayes loves the Bay of Islands, particularly picturesque Elliot Bay, Ms Edwards says Rotorua is her favourite spot, as "it's so different from anywhere else".
Despite their love for New Zealand and Esme holding citizenship, Ms Edwards says the family won't be moving yet, because as a nurse, her career prospects are better in the UK.
"Esme's walking around in the grass and she just loves it - it's like a new sensation for her. And it makes me sad because we can't offer that in London," Ms Edwards says.
"There's just such a vast amount of different landscape. You've got glaciers, you've got Fiordland, you've got tropical beaches, you've got mountains and you can go skiing - there's not many countries where you can do all of those things."
Though some people have commented that Esme is unlikely to remember much of her travels when she grows up, Ms Edwards says she still benefits greatly from all the different experiences she's had in her young life.
"Although I felt we didn't have enough toys on our first trip, she was still stimulated by things around her.
"In Asia she likes walking through the markets, because you get so many beautiful prints on fabric and cushions and it's all really colourful and stimulating for a baby.
"We had been at home for a few months between our travels and sitting at home you can just tell she's bored."
Ms Edwards said she had received some negative comments online as Esme had been too young for travel vaccinations, but the couple had been well-prepared before embarking on the trip.
"We were extra careful with water, I was breastfeeding and giving her probiotics and we avoided malaria areas as well.
"[As a nurse] I felt a bit more comfortable in managing a situation if it were to arise, in comparison to a mum who's not medically trained."
And now that Esme is a toddler, there's a whole new set of challenges - including being that family on the plane no one wants to sit next to.
"You can just see people looking and thinking 'please don't sit next to me'. And that's understandable, I used to do the same thing when I was single and didn't have a kid."
But for now, despite the challenges, it seems there's one more young traveller in the world who's definitely caught the wanderlust bug - and we're looking forward to seeing the next series of pictures.
• Follow the ongoing adventures of Karen Edwards and her family on the Travel Mad Mum blog, her Facebook and Instagram.
- nzherald.co.nz