If I were you I would make a list of all the issues and give it to your GP asking them to refer you to the paediatrician. If you can also discuss any problems with the school to see what they have to say then that would be good too.
I also agree, make notes on the behaviour that concerns you and request a referral to see a Developmental Paediatrician who will be able to see beyond the obvious.
My 4.5 year old was initially thought to have Dyspraxia, at 3 years old but has just now received his official diagnosis of ASD. In addition, he has some hyperactive-ness (if that is a word), for which no diagnosis has been made but I'm in the process of getting a referral to look at this too.
As Ineedmorepatience says, the overlaps are considerable and it's always best to seek more professional help in getting clarity.