My question is - what should my timeline be for everything?? Should I set up a coop, move in the older hen, let her get used to the new home, see if she will sit on some wooden eggs, and if she will, try putting the babies under her?
Not quite like this...
If you want to take her, that's very kind of you. How old is this lady?
Has she actually gone full broody in the past and successfully hatched and raised chicks?
There are a lot of things involved and everything depends on the hen and they all have different personalities and temperaments so you really can't tell what she is going to do.
First, if you want chickens you need a proper setup for them. They need 3.5-4 sq ft of space per bird, 1 linear foot of roost space (with the correct amount of distance from the walls and other roosts set at the correct elevation) and as close to 1 sq ft of permanent ventilation per bird in the coop. The run needs to offer ideally 15 sq ft of space per bird.
If you already have such a set up, excellent! You can bring her home and get her set up. If not, build it. I found the easiest thing to do is to convert an older building like a shed into a coop. If you want ideas on this, you can click on the My Coop link under my username or research other coops and get building.
Once she's settled in, you can create a nice cozy floor nest for her in a semi-private area. Regardless there are no other hens to bother her, they instinctively prefer to "hide" the nest. From predators.
A hen is not likely to go broody if she is stressed and moving her will stress her.
She may or may not go broody. If she does and locks down on her nest of fake eggs, I'd wait at least 2 weeks, preferably 3 before giving her chicks (that you slip under her well after dark and remove the fake eggs) and the chicks should be less than 1 week old.
If she doesn't go broody, you can set her up in the coop and construct a built-in brooder, get a brooder plate and raise chicks with her in the coop so she can watch them grow up and they can see her. When the chicks are about 3-4 weeks old, you can fashion some chick size doors in the brooder so they can come and go but she cannot get in and let them start to mingle.
She may even leave them alone because she is a lone hen.
Start immediately feeding her a good quality all flock type of feed that offers 18-20% protein and 0.7 - 1.3% calcium on the tag. Put out a container of oyster shell on the side for the hen to consume free choice. Feed this for life. Feeding this way is the best as it allows appropriate nutrition for all stages of not only a hens life, but pre-POL pullets and cockerels/roosters. Nothing ever needs to be changed.
I have one Australorp. She goes broody every single year and has hatched for me all but the first year. She is going to be on hatch duty again this year when she turns 6 years old. She is still laying eggs. She is rock steady and good mother with a calm demeanor but 'take no BS' attitude. So much so, she even adopted another hens chicks to raise with her lone chick.
I'm not saying that the Australorp you are interested in will be the same but perhaps it is a strong breed characteristic. Maybe it will work out for you that she will brood. But I've provided what you can do as an alternative to that.
Good luck.