The Inverness native told MTV News that several startling secrets will affect the couple's bond as well as their relationship with The Doctor (Matt Smith).
"At the end of the last series of Doctor Who, we saw Amy get married, which was a long-running story arc… It seems kind of fairly settled that now's there going to be this trio of people in the Tardis," Gillan said. "So that's where we pick up in the first [episode 'The Impossible Astronaut']."
She added: "It's interesting to see the affect that marriage has had on all three of the main characters and also it helps define Amy's relationship with The Doctor. Something's going to happen to do with this marriage that's going to change the course of everything in this series.
"It's going to get quite dark. Everyone's got a little secret from one another, which I think is quite interesting. Amy's got a big one!"
Gillan went on to dismiss the suggestion that any rift in the marriage will be due to Amy taking a romantic interest in The Doctor, adding that the two characters work best as friends.
"Rory's the one for her," the star remarked. "Also, Amy with The Doctor - what would that even be like? She's as mad as he is and they wind each other up so much... So I think they're best off as best buds."
While The Doctor first met his latest companion in the fictional English village of Leadworth, Amy is the first full-time Scottish companion since Second Doctor cohort Jamie McCrimmon (played by English actor Frazer Hines) left the Tardis in 1969.
The sixth series of Doctor Who premieres on April 23 on BBC One in the UK and BBC America in the US.
Watch the latest Doctor Who trailer below: