I have that cage for my cockatiels. As far as size goes, sometimes I have 5 tiels in there, but most often 3. Plenty of room for them. It is much lighter than a larger parrot cage, so easier to move around.
The things I don't like about it are:
1. The bars bend easily. Especially hanging something heavy from the top.
The bars are thin and spaced close together.
2. There are 4 small side doors. They are spring loaded and are too easy to push open, so you'll have to do something about that. I zip tied all of mine because I use the large front door to do food, etc.
3. The 2 lg. front doors are super easy to open also. All they need to do is push up on the long bar and boom, the door is wide open. I've put a second lock that they can't open, but it's a pain for me to. If you are in and out of the front door alot, (which I am) it takes longer to get the door open.
4. The feeder dishes that come with it are garbage. They don't fit between the slates.
I bought mine on sale for $118. I originally bought it for an 'outside' cage. During the summer, I bring them outside when the weather is nice for the day. Their other cage is so large it won't fit through my door. Now that I am fostering a amazon parrot, he took over the larger cage and the tiels have the smaller one.
I don't know much about quakers, but as far as room goes, I think it would be ok. Not sure if your bird can bite through the bars though. This is just my opinion, maybe someone else can chime in.
Betty.
PS. Just thought of something else. Because the bars are so close together, it will be hard to put a larger perch in there. That's another reason why the bars get bent.