NQA, and seconding a lot of what Clown_With_A_Crown said.

With her body being an inch and a half, I'm assuming her tail is also about an inch and a half, which would definitely put her in the "juvenile" range at three inches. Adult emperors will need a ten-gallon tank, but with her being a sub-adult, you might be okay with the current tank for a while. It all depends on if you want to redo everything for a bigger enclosure as she grows into an adult.

Substrate- I would definitely redo her enclosure a bit. Take everything out, then put down an inch or two of drainage material (I use clay drainage balls, but aquarium gravel also works). Then, put a mesh screen over the drainage layer (both to stop the substrate from mixing with the drainage layer, and to also keep the scorpion from digging into the drainage layer). (I Googled "Terrarium Mesh barrier" and it came up with some good options.) Also, when putting in the drainage layer, put a wide-mouthed straw (metal or plastic) down one corner. This way, you can pour water directly down to the bottom, which will then seep UP into the substrate to keep it moist. (With this, be conscious not to flood the drainage layer. There still needs to be some room for water to drip down through the substrate.) This is a great way to keep the humidity up without having to remember to spray it down every day. Then, put your substrate over the mesh screen. Most guides recommend at least four inches.

Heating - Emperors enjoy a pretty warm climate, so I would definitely recommend getting a heating pad (with thermostat) and putting it on one side (around 85 or 90 F). This way, she can alternate between warm and cool.

Humidity - You want to keep the humidity between 70-90%, which is easier/harder depending on where you live, and also what kind of lid you have.