what Edam says is true - and Andrew Wakefield was demonised unnecessarily.
A similar thing happened to a researcher in GM crops, Arpad Pusztai, when he discovered that using snowdrop lectins in potatoes caused problems in the rats that were fed the potatoes - he published in all innocence and was removed from his research post and all his work rubbished by his colleagues from then on.
The scientific establishment is a very political arena, not least because of funding issues - there is no "pure" science these days. Most, if not all, labs in Universities are funded by pharmaceutical corporations and they are more likely to look kindly on research that doesn't rock the profit boat.
One place you can try for more answers is the Austism Research Unit at Sunderland University, headed by Dr. Paul Shattock, himself the father of an autistic son.
Another researcher, a Dr. Rosemary Waring of Birmingham University, has written some interesting papers on the types of children more at risk from vaccines than others. Risk factors include a high allergic history in the family - i.e. family history of eczema, asthma, rheumatoid arthritis, migraine, autoimmune diseases. Dyslexia, dyspraxia and ASD in the family might also increase risk.
If your child has a good diet with plenty of vitamins and minerals, has good bowel bacteria and is generally healthy, they are unlikely to suffer ill-consequences from the MMR - but they might, as they might from any vaccine.
I have this decision to make for my DS very soon and have already decided not to give him the MMR as he didn't much like the PCV vaccines; so it is good to know that there are still docs prepared to give the measles vaccine separately. I will be getting that done for him in the next 6 months and then the others before he is 2.