pattymac, I broke down last year and bought a tree, I bought a fake one, the first fake I've ever had. It was tough to do that, but I'm past the real tree warm and fuzzies now.
I used to take my son out every year and here in BC that meant normally hiking through fields of mud to pick out and cut down the perfect tree. You'd slip, fall, get filthy, drink hot chocolate and then go home and curse the tree that wouldn't stand straight, fight with the knotted strings of lights, drop and smash a few ornaments, then on Boxing day pick the tree up off the ground after the dog and kid ran under it and put it all away until the next year!!
Loved it then, now, yup, I'm past that. But I did want a tree. I also bought lovely, but non-breakable ornaments for the tree on account of the dogs. Of course the grandson isn't an issue this year, but by next year he will be, so plastic is fine.
Good luck to you, the critters will be fine. My cats never bothered the tree at all when we had them (tree's and cats...). With the dogs it was just their tails that got them into trouble.
Ah the good old days....