I have a Eucalyptus caesia 'Silver princess' it's dying and I suspect a soil fungus is the issue.

Thank you for contacting Yates. 

We won't be able to tell if the tree is affected by soil-born fungal disease from the picture.  An easy way to check if plants are still alive is to scratch the stem. For a living tree, this should be lime green, in a dead tree it is dry and brown. 

As for Anti-rot, it is only registered as foliar spray but not soil drenching. 

Meanwhile, it is beneficial to help adding 'Yates Dynamic Lifter Liquid Concentrate' as a gentle fertiliser and soil improver. It's certified for use in organic gardens, and contains seaweed, blood&bone and fish meal to help developing new roots and restoring healthy growth. Click here for more info on this product: https://www.yates.com.au/product/garden-fertilisers/certified-organics/yates-dynamic-lifter-liquid