I was emetophobic starting age 8 and it was awful. Sorry you have to go through this. Emetophobes can eat and enjoy food but only under the guarantee that it won't make them sick. So I always had a list of "safe foods" and eating from there didn't trigger anxiety.
Obviously from a therapy pov it's not ideal to encourage making lists of "safe" and "unsafe" things but if the alternative is literally starving then it's better than nothing. Since 8 is still fairly young you have the advantage that they will believe what you tell them. If you emphatically say that certain foods are safe and will not make them sick, then it becomes easier for them to integrate those into their diet. From my own experience, these are good ones to start:
Perfectly ripe bananas. Absolutely no chance anyone can get a dodgy tummy from an unpeeled banana. Underripe ones might be too starchy and cause GI symptoms so best to avoid those for the time being.
Crackers or crisps
Plain toast with butter
Plain noodles with butter or jarred tomato sauce
Very well washed (or peeled) apple slices
Shelf stable puddings, chocolate bars or biscuits
Foods to avoid are any that could inadvertently cause GI symptoms (fizzy drinks, high fat, spicy, high lactose, high fibre etc) or any that are typically connected with food safety issues (bagged salads, raw produce, seafood, shellfish, cold meats etc).
There's a lot of irrational thinking in emetophobia so you need to offer lots of reassurance that the foods are fresh, show them the cooking process so they can see there's no cross contaminations and that everything is well within the expiry date. Don't use any open packages that have been stored in the fridge for a while. Again, these are typically emetophobic behaviours that therapy aims to eliminate but if you are in an emergency situation right now, then it's better to lean into the thinking than attempt to do too much too early.
By given them reassurance, you indicate you understand their thinking patterns and are willing to work on a productive meal plan together. I strongly encourage looking into the Thrive Program by Rob Kelly is which is the closest accurate solution to emetophobia. CBT, hypnotherapy and other types of talking therapy are virtually useless against this phobia.
At the root, emetophobia is about control and psychologically very similar to anorexia. It becomes a bit easier to understand considering how prevalent anorexia is and how often it affects young girls. Instead of a fear of gaining weight, emetophobia tends to hit girls who are easily disgusted and hate the "grossness" associated with being sick. These are girls who are most likely slim to begin with (hence less susceptible to anorexia) but with the phobia, many tend to remain skinny into adulthood.
There is also a significant overlap between neurodivergence and emetophobia. If your DD hasn't been assessed for ADHD or ASD and you feel that might be an issue, then definitely worth getting it checked out. Symptoms tend to improve immensely if co-morbid conditions like ADHD get treated using medication.
If it's any consolation, I underwent lots of therapy in my 20s, did the Thrive program and eventually managed to reach a point where the phobia doesn't affect my life to any significant extent. During school & university I was essentially surviving on a diet of the foods mentioned above, but nowadays I eat virtually anything and have no problems with restaurants or travelling. I also went through pregnancy, birth and took care of a refluxy baby.
A lot of that was self-realisation and reaching a point where you don't want to live within self-imposed restrictions anymore. My parents were totally oblivious to it all and I wish I had their support and awareness earlier. Most of the therapy options were through my own research and I also realised much later I have ADHD so that explained a huge amount of the disordered thinking that fuelled the phobia.