We just bought a house and are closing in two weeks. (yay!

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We have quite a large backyard, so I had an idea. Let me know what you think.
I was thinking about putting up a chainlink in a smaller area. The back door would lead right out to it. The back of our house comes out in a "L" so I would only need to put up two sides connected to the house. It would be about a 20 x 20 foot area. Maybe a little bigger. THEN, we are putting up a wooden privacy fence around the whole yard. So the smaller chainlink area would be inside the larger fenced area.
Of course, she would only be outside with me watching so she could potty or run around. I just think it would be safer for her this way and easier for me to keep an eye on her. Plus, my son could play in the bigger part of the yard without worry of stepping on her. Shes just 3 1/4 lbs right now at 5 months old.
What do you think?