Hi, I too have lots of ivy disguising my fences. I tried to keep Max away but he was very interested in it and has certainly eaten lots of leaves and stems. Luckily he has been fine and grew out of it so I haven't had to remove it. He's had a few tulip bulbs too!!
When they are small they seem to want to chew and pick up everything in the garden, but this does seem to have stopped now. Also Max likes to carry a ball around in his mouth which prevents him putting anything else in it!!
I would be interested to know how poisonous it is supposed to be as we are moving soon to a brand new house and I do like covering my fences with something.