how much space do i really need for a single bird?

So I'm considering my coop options. I just have one chicken. Shes still inside now, and for a few more weeks.
When she does move outside, she'll have full run of my small backyard. There is a 6 foot fence all the way around, so i'm confident she'll be safe out there.
I was actually thinking of converting a dollhouse into a coop/ nest box, but I'm just not sure if that will be big enough. There would be about 4 sq feet inside, enough for a nest box, and a place to roost.

I live in So Cal, near the beach. It never gets very cold here, nor very hot. generally around 65-75 year round.

What do you guys think?
is that enough space?

 

I can't unfortunately. I have an HOA. We're not supposed to have poultry, so the only way that I can have a chicken is if she is one of my 2 household pets.

I mostly work at home though, and I'm hoping that the diaper harness I ordered will work out so that she can have the run of the house with me and the cat all day when I'm home.

I might try to sneak by with another one in the future. I want to wait a while and see how it goes with one first though.