The ketogenic diet has NOTHING WHATSOEVER to do with ASD - why you might have considered it confounds me.
The ketogenic diet works essentially on the basis of starvation - like on old-order anti-epileptic drugs, therapeutic levels of drugs are determined by blood tests, the ketogenic diet is not considered therapeutic until the child is in moderate-severe ketosis, or clinically starving. This is not a diet that can be "introduced" - it MUST be initiated while inpatient. ALL sources of carbohydrates of any form are withheld until severe ketosis has been achieved, and then the fat and protein based diet starts. The child is not discharged until he or she is in constant ketosis consistent with their treatment plan, their liver has stabilised from the insult from the diet, and their weight loss is stabilising. Many children leave the hospital off the diet is it is that hard on their bodies.
Any neurologist who would recommend that course of action (or frankly, declare that a child is "definitely having seizures" after seeing unusual movements that had been occurring for only one day) after meeting them once and not doing any sort of investigation is foolish at best and negligent at worst. If one suggested it to me before medication trials, I would pick up my belongings and walk out of the office without another word.
I have seen neurologists "fooled" by non-seizure activity many times - I have never seen or heard of one that would make a declaration like that out of hand, for the very real reason that they could be very wrong, and that parents hang on to what they say very tightly when they are stressed and upset.
Bee has been on 11 different medications, and still has dozens of seizures a day. I was told when she was a toddler that while we could consider the ketogenic diet (after her 4th or 5th medication failure) the consultant strongly recommended that we go home and research it well before we jumped into anything. He explained that the formula was vile (it is) and he had never seen success with a child who did not have a gastrostomy tube, as the amount of formula or food required was precise, and it had to be consumed completely. Doing the diet orally, he said, particularly with a child who has a neurological compromise (you stated your DS has ASD) was nigh impossible, as they will resort to pica, food seeking and theft to get what they are craving. If, after all this and our research, we still wanted to consider it, we would need to be referred to a special centre to have it initiated. This is NOT something that is offered out of hand and certainly NOT without medication failures. Even Epilepsy Action UK says this.
We saw a new neuro this year - Bee's regular epileptologist (200 km away) wants her to have someone local to help in a crisis. When we talked with her, after going through the last 7 1/2 years of Bee's meds and seizure history, and the fact that she has a "malignant" epilepsy, she asked if we had considered the ketogenic diet. Before telling her what we had decided 5 years ago, we asked her what her opinion of it was. She felt the way the first neuro did, and Bee has a gastrostomy now. For Bee, primarily because of her impulse control issues related to her ASD, she said she might recommend pursuing vagus nerve/deep brain stimulation before the ketogenic diet. Clearly, it is not the same as trying the GAPS diet or going GFCF.
As for carbs - you would be surprised what there are carbs in. This isn't the Atkins low carb/high protein diet, this is a diet that is primarily fat (true ketogenic diet is 80-90% fat, 10-20% protein and no carbs). When a child is on the diet, even a small amount of carb in a dose of Calpol or Neurofen can kick them off and cause status seizures. Things are calculated to 0.01g.
The ketogenic diet is a medical act, doing it part way achieves nothing. Doing it without medical supervision is dangerous.