Hannah Godwin initially was torn between Dylan Barbour and contestant Blake Horstmann

From the moment he set eyes on Hannah Godwin during Bachelor in Paradise, Dylan Barbour was unabashedly smitten. But now that they’re happily engaged, they say they won’t rush a wedding.

“We are both so overjoyed to experience this [engagement] chapter together,” Godwin, 24, tells PEOPLE. “Especially since the first chapter was pretty quick. We’re really excited to enjoy being engaged.”

But Barbour, 25, jokes that he wouldn’t rule out spontaneous nuptials.

“We’re getting married in Vegas tomorrow,” he says with a laugh. “But I am really happy. We’re just going to enjoy what we have right now and take it one day at a time.”

Credit: Craig Sjodin/ABC via Getty

Godwin initially was torn between Barbour and contestant Blake Horstmann, whom she had met before Paradise. She says she ultimately fell for her fiance’s strong character.

“His words and actions lined up,” says Godwin of Barbour. “He would say these things but he would also show me. Our personalities connected. Romantically were very attracted to each other, but I also see him as somebody I can spend every day with and laugh with and who can be my friend. And that’s really cool.”

And despite her initial struggle, “I realized that whomever I gave my rose to, I wouldn’t want to leave without,” she says. “And that was Dylan. As soon as that clicked, I was all in.”

Credit: John Fleenor/ABC

Now, Godwin plans to move from Nashville to Barbour’s hometown of San Diego, and though the couple aren’t moving in together yet, “we will be seeing each other a lot more,” she says. “I’m definitely getting a place with him in mind coming to stay all the time!”

As for eventual wedding bells?

“We talk about the future all the time,” Godwin says. “But we’re really taking in this moment, too — and living it to the fullest!”