My daughter has CFS she was diagnosed some months ago but our doctors couldn't suggest any ways to constuctively help her.
We have discovered that it is absolutely essential that the sufferer regulates both the quality and interval of food intake.
Breakfast, mid day meal and evening meals are all absolutely essential and no huge gaps should exist between them.
We recognise through our daughters experience that CFS takes hold of the sufferer in such a way trying to convince the sufferer to be indecisive about their food. If you recognise this you will help beat this debilitating condition. Work on this basis and as soon as possible take exercise gradually. Dont rely on just getting enough food to stave off the weakness for a short time, work on the basis that you need to make your body want its food, so go a little extra distance with the gradual exercise whenever you feel able to.
Our daughter was a wreck 6 months ago, but we recognised that her weakness was due to her irratic behaviour towards her food. She still has the odd bad day but usually only if she goes too long without her food or if she skips a meal.
If you understand how the CFS takes its hold you can control it.

I'm glad that you have decided to try proactively helping your daughter, but I'm afraid she might need much more than an eating plan if she has been diagnosed with CFS. The major national sites tell you "there is no treatment, there is no cure" which is very defeatous. I was diagnosed 3yrs ago and have actively sought anything to help. Your daughter will likely follow one of two CFS patterns. Some gradually get better in 3-5 years, inexplicably or with only moderate assistance such as your eating plan. The rest slowly get worse. Symptoms progress including increased fatigue, brain fog (forgetfulness, short attention span), sleeping disorders (waking every 2 hours, isomnia, sleeping 16hrs at a time), and many other symptoms,even if they seem subtle. Eventually the immune system will start to shut down and every cold, flu, and random infection will slowly start to set in and while doctors will treat each one individually prescribing the various antibiotic here or there, none will help the underlying problem... CFS. There IS help and there ARE doctors who actively treat CFS. They are just hard to find. There is a protocol for CFS called the Tietelbaum protocol and it is outlined on the web and in a book by Dr. Tietelbaum called "from fatigued to fantastic." I encourage you to read up on this protocol as it has helped me immensely over the last 6 months and some of the treatment may help your daughter's quality of life even if she is feeling somewhat better at this point. The book is written in such a way that you can take it to your general doctor to assist with treatment. Good luck to you and kudos for helping your daughter.