I like the shoes they've teamed it with and a light tan clutch bag or similar and not much else. I think a chunky necklace would look like you were trying too hard.
If you didn't want to go matchy-matchy with shoes and bag, I do have a bag that is white with really bright pink and green circles on it that would go fab with that dress (picking up the green of the dress). You might need to take the dress with you to the shops though if you were taking this avenue.
I also think big button type earrings would look good. Dangly earrings might look a little twee,