Hi I just moved into my home here in Iowa last year but this year I noticed a vine like plant growing on a large part of my fence... I have a pug who thinks everything is food so I would like to know what this is and if it would be harmful to her... Thanks so much.

I'm not really sure but hopefully someone will recognize it and be along soon to offer suggestions. It kinda reminds me a bit of Wild Buckwheat (Fallopia convolvulus) but I don't know if that grows in your area.

More images for comparison:
http://www.illinoiswildflowers...
http://www.luontoportti.com/su...
http://climbers.lsa.umich.edu/...

I forgot to say, if it is in the Convolvullaceae family, it does have toxic qualities. http://www.aspca.org/pet-care/...