Hi OP
I had a very good look into this as my DS aged 2.9 has autism and I wanted to know the chances of any future children having it.
We went to see a geneticist who examined my son for any subtle physical features which might suggest a genetic abnormality (there were none). She then said he could have a blood test where they would do a test for fragile X (a condition associated with autism) and an array test which I think isn't looking for any particular gene but more any strange patterns or inconsistencies on a macro level (she described the array test as looking at a whole library of books and looking for shelves which might have fewer books, or too many books, or books stacked strangely, compared to the rest of the library!).
She did admit however that it was unlikely they would find anything that would pinpoint why my DS had autism. As a PP mentioned above - I think it's more to put the results into a very large database and hopefully one day that will help come up with answers as to the causes of autism. Because of the low chance of actually finding anything, I couldn't bring myself to put DS through the blood tests as he is so little. If he ever does need blood tests in the future for any other reason, we'll get it done then.
The geneticist told us that without doing the tests and with neither me nor DH having any history of autism in our families, the statistics said that the chance of any future child having autism was about 15-20% (I imagine a bit higher if a boy and a bit lower if a girl). However, this is not like cystic fibrosis or sickle cell anaemia where they can look at your genes and say, right, each of your future children has a 25% chance of having that condition (a bit like it's possible to give a set percentage chance of having a child with blue or brown eyes). This is just a statistic. For some people, looking at their family history and genes, they will have a much higher chance of having autistic children. For some, the chance of it happening again will be miniscule. Thing is, they generally just don't know who will have the higher or lower chance because they don't yet know what they are looking for.
Also, as others touched on above, a genetic abnormality does not necessarily mean that it was inherited - genetic mutations can occur spontaneously at conception and have nothing to do with the parents' genes.
And as for your doctor saying children aren't born with autism... well, I think most medical professionals would strongly disagree! I am sure my son was born with it.
In any event, the general consensus is that autism, in most cases, is caused by a combination of genetic and environmental factors (as I'm sure you're aware, theories abound about environmental factors that may play a part, such as pollution, medication, oxygen problems at birth - the list is pretty long and, in many cases, just guess-work).
I'll finish by saying that after much deliberation, we decided to go ahead and have another child and I am currently 6 months pregnant. We figured that even if the next child is autistic, he/she will still be a lovely brother or sister for DS. DS's diagnosis absolutely devastated me but 18 months on we are all generally pretty happy (especially DS who is one of the sweetest and happiest children I know). I remember at the time, when I was not coping at all, speaking to one woman at the National Autistic Society who had three children, the oldest one of which had autism. She said to me "You know, you don't love them any less - in fact you love them more". And that stuck with me and I know it's true for me too.
Good luck to you - I know this time isn't easy.