In the UK you would need a referral to see an orthoptist (they're like gold dust), via GP and a letter from the optician would speed things up. However, you can see a behavioural optometrist privately.
In Italy I would imagine you walk into the opticians and just ask. Good opticians would have both an 'ortoptista' and an 'optometrista comportamentale'. Just ask for their 'prassi'. Of course via an optician these specialists are private, but it's worth asking how is an ASL referral pursued.
I'm not sure how much a pediatra would know about dyslexia (in the UK zilch) but they might know how to refer to an educational psycologist who would assess for dyslexia and the pediatra should know the ASL referral route. I would imagine the paediatrician would assess for dyspraxia which often accompanies dyslexia ( a terapista occupazionale would deal with this). I would hope the pediatra would also enquire about any auditory problems as Auditory processing disorder (APD)can accompany dyslexia (the best specialist for this would be un pediatra neuro audiologo).
I hope am not alarming you. I'm just covering all bases. Ime the medical profession in Italy either acts as if on an extended siesta or it's all over you like a rash 'e ti girano dentro fuori come un pedalino';)
With a little luck you'll only need a logopedista (Speech and Language over here) to establish an action plan and/or a few minute intervention support. :)