A fairly inexpensive short term solution would be to do what I've done with Bailey's potty area - but on as large a scale as you'd like.
Go to your nearest Home Depot (or any such place) and get rolls of hardware cloth. That name has always amazed me, because it's actually very heavy duty wire mesh. I got a roll that is 1/2" mesh 24" wide by 25' long for $17, or $0.68 per foot. If you think your baby can clear a 2' high fence, it also comes in 36" wide. Throw in as many landscape grade stakes as it will take to hold it in place (at $0.28 each) and you have a fairly inexpensive fence. It doesn't show up strongly, but you can see it behind Bailey in this picture.
When Bailey gets past the potty training stage, if we want to give her freedom to roam the entire back yard I'm going to attach this to the bottom of the fence all the way around.