Not so much that you will drive yourself insane, but enough so you know what you are looking for and to be sure that you are well informed. Preparation and knowledge are the key to getting anywhere in appointments.
Complete this questionnaire at ChildBrain - IT IS NOT A DIAGNOSTIC TOOL - but a very in-depth questionnaire that will advise you whether or not you should visit a doctor. It's quite challenging to complete and I would recommend you set an hour aside to do it, so you can click each question and view the scale before answering. Print off the results or re-write the questions/characteristics that are of concern to you. Keep a copy. It is a great way of making sure you have remembered everything in an appointment, and also a good way of having on file what your child's difficulties are without relying on a strained administration department.
Visit a health professional. This could be your Health Visitor and/or GP.
If you already have and are not getting anywhere, but are genuinely concerned, with reason, then you can request another GP or attend a 2.5 year development check up at a local surestart children's centre. Your child should be 2 for this and you can find the centres near to you at SureStart's Gov Site. Not all of the centres have the check up, but some do. It is with a community paediatrician (good). Call those that you can get to and try to arrange it. Had I known this sooner, I would have gone straight down that route! Surestart centres are there specifically for you and can help you with almost everything related to a child under 5. At this check up, you're child will be assessed for whether they are age appropriate in development and you will be asked questions. It is up to you whether you would like to raise ASD as a suspicion or leave it to the paediatrician to see if he notices anything and then ask at a later point.
If the children's centre is not an option, then talk to the GP again, be up front and say what you want and need. If your child is in Nursery or Pre-school then this is a good way of getting listened to too. Ask to have a meeting with the SENCo and discuss your concerns, it is likely they have been monitoring your child closely anyway. The SENCo can bring other professionals into your child's life and you can take it from there, or you can ask for a report to be written to take to another doctor/paediatrician.