Kim Kardashian and Kris Humphries
08/25/2011 AT 06:00 PM EDT
and Kris Humphries' post-wedding trip to Italy's Amalfi Coast
is apparently just a mini-honeymoon, and the proper one will come sometime down the road, Kim tells PEOPLE.
The trip had to be a quick one since Kardashian is due back in New York within days to begin filming the second season of Kim & Kourtney Take New York.
She's also expected to attend the Video Music Awards in Los Angeles on Sunday.
"We want to take our big honeymoon later," says Kardashian, adding that the destination would be "definitely tropical."
seem to be enjoying their current trip. They've been spotted smooching on a lounge chair and dining on the terrace of their hotel in Capri.
will air a two-part special, Kim's Fairytale Wedding: A Kardashian Event
, on Oct. 9 and 10, only on E!For exclusive personal photos from Kim's fairytale wedding and all the details, pick up the new issue of PEOPLE, on newsstands now
. Click here
for a special $1 off coupon.