My little Graysee does the same thing. Our yard is fenced, too, but it's heavily landscaped, and I have to be diligent to inform her of what to stay away from. She is pretty good, as she moves away from something immediately if I say "NO EAT!". There is a good list of harmful plants somewhere on this site, but I'm not exactly where I saw it, so I'll try attaching my own version here, if I can find it. I suggest just monitoring your pup until he/she learns what's off-limits. But, I still have to chase mine sometimes to get something away from her; I think she believes we're playing!
