My kids had eczema too, and I found the organic care range (available at Coles and Woolies, inexpensive) was good for us.
The dinosaur and princess shampoos double as bubble bath or shower gel, or they make a shower gel that also bubbles up nicely in the bath.
We did try a range of others, but this one seemed the best. Some of the others are based on SLS or coco betaine, neither of which are good with eczema.
Any bubble bath can be a bit drying, so perhaps use on an occasional basis (like when she is really dirty!) and use oil the rest of the time.
Hope that helps.