“I just want to make sure Lauren is happy. If it were up to me, we’d get married tomorrow!” Arie Luyendyk Jr. tells PEOPLE

Their Hawaiian wedding is just five weeks away, but The Bachelor‘s Arie Luyendyk Jr. and Lauren Burnham are still working on the finishing touches.

“There are still some things that are up in the air, but we’ve got the major boxes checked,” says Luyendyk, who got engaged to Burnham in March. “I just want to make sure Lauren is happy. If it were up to me, we’d get married tomorrow!”

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With the help of famed jeweler Neil Lane, Luyendyk, 37, and Burnham, 26, recently selected their weddings bands.

“I had my eye on mine from the beginning,” says Burnham of her 4-carat eternity band, set with over 200 round and French diamonds. “I love diamonds, what girl doesn’t?”

Image zoom Neil Lane Couture

Image zoom Neil Lane Couture

And Luyendyk admits that his ring, made of platinum and rose gold, has some Bachelor history. “It’s the same one that my buddy [former Bachelor] Sean Lowe has,” he says. “I don’t mind. It’s a good omen!”

After the wedding, Luyendyk and Burnham have another exciting occasion to look forward to — the birth of their baby, due in June.

“We’re so excited,” says Burnham, who says that despite “really bad” morning sickness, things are going smoothly. (They know the gender but aren’t revealing it yet).

Image zoom Arie Luyendyk Jr. and Lauren Burnham Jana Cruder

As far as the timing, “everything is happening so quickly,” Burnham admits. “But everything has been quick, so it’s kind of fitting in that way!”