Ask Mr. Smarty Plants

Below are five suggestions of vines native to Kansas for the identification of your plant.  Only the first is reported to be toxic.  Hopefully, what you found is one of the non-toxic plants so that you don't have to worry about your dog eating the fruits.

The fruits of Menispermum canadense (Common moonseed) are reportedly highly toxic according to the Poisonous Plants of North Carolina.  Here are more photos and information from the Herbarium at University of Wisconsin-Green Bay.

There are two species of Smilax:

Smilax herbacea (Smooth carrionflower) and here are more photos and information from the Plant Diversity Website at the University of Michigan.

Smilax lasioneura (Blue ridge carrionflower) and here are more photos and information from the Plant Diversity Website at the University of Michigan and from the Freckman Herbarium at the University of Wisconsin.

Smilax herbacea is on the "Plants Non-Toxic to Dogs" list on the ASPCA Toxic and Non-Toxic Plant List -  Dogs.  Smilax lasioneura is not on either the "Plants Toxic..." or "Plants Non-Toxic..." lists.

There are two grape species:

Vitis riparia (Riverbank grape) and here are more photos and information from the Herbarium at University of Wisconsin-Green Bay. 

Vitis vulpina (Frost grape) and here are more photos and information from Duke University.

Neither of the Vitis species occurs on any toxic plant list that I could find.

If none of these are the vine you saw, please visit the Plant Identification page to find links to several plant identification forums that will accept photos of plants for identification.