The testing is expensive. The cheapest you can find is a couple hundred dollars if you get it done at the psychology dept. at a University. The money for testing is often better spent on education, toys, or taking a family trip. Most people pay for testing when there's more than just the information of tge number to get from it, such as enterence into a program.
Also, I don't know that you necessarily have to switch doctors. Technically they're the doctor and you're the parent so even if they don't see your childs personality like you do or would make the parenting choices that you do, as long as they are competent at their job, which is to treat your childs health, then you can agree to disagree. Of course if you're not happy you can shop around for a different doctor.
At around two I started teaching my kids handwriting lessons using Kumon tracing (like mazes for toddlers), then Kumon alphabet games. I put crayons and paper in their hands as infants. I used the Kumon with them as toddlers, showing them how to use a fat marker and follow my finger through the mazes because a marker writes smoother than a pencil. To each their own and some people said it was wrong to teach a child so young formally but I thought it would be less frusterating as they grow if they could easily express themselves. Many toddlers also like Starfall online if you like electronics for young kids.


Youth lives by personality, age lives by calculation. -- Aristotle on a calendar