My daughter put her tree up on a table. Perhaps yours is too tall for that? Another idea, if the tree is tall, is to put it behind a large piece of furniture. Plastic ornaments on the bottom is a great idea. She'll be cute as she checks them out with your supervision.
You're right to want to keep the tree out of her reach. it would be easy for her to pull it over on herself. I like the play pen idea. You could find a large piece of card board at a store that sells large appliances if you want to go that route. However, couldn't she pull that down?
You could put the tree in a room that you could block off so that she isn't able to go into the room by herself.
I grew up with real trees which were always table top size when my brothers and I were young.