She looks to be enjoying that wheel! I am sure she will enjoy the Alaska cage as well. Don't mean to put a damper on the ball but they can be a bit risky as the rat balls have such large slits - hammies can get their toes or toenails caught in them. I gave up on using a ball. I do have a Savic Rat ball (it seemed to have the smallest slits of all but they are still too large) - I just use it for transporting our hammy from the cage to a playpen area now. You could rig up a playpen maybe, rather than using the ball. There are lots of tutorials on making one, or Zooplus sell a good one but it's about £25. I think there are cheaper options. Or you can use the bathtub (dry with plug in) for taming and running around although it's not really big enough for a playpen.
I made one out of sheets of correx (plasticised corrugated cardboard) and bulldog clips from a tutorial on here. That did us for a while but it wasn't escape proof so I had to keep an eye on the corners. Or you could make one from sheets of cardboard from large cardboard boxes and bulldog clips.
This was my old playpen - you can set it up any shape you want - long and thin or square. I used A1 sheets of correx/coroplast. But to be honest that cost me about £25! Same as the Zooplus one. I have the Zooplus one now and it's great.
https://www.youtube.com/edit?o=U&video_id=AvXJ-Jbo0CM
Skyline Ranch Arizona Indoor Run | Free P&P £29+ at zooplus!
Someone on here made one out of some panels you can get that clip together and aren't too expensive I think. When she's tamer you might not need one. Our hammy used to run around on the sofa when he was tame - I just blocked the front edge off with a blanket and kept an eye on him.