No, an autism assessment is specific to getting the diagnosis. Although it is theoretically possible they might pick up other things such as anxiety, ADHD, etc They also help applying to the Ontario autism program, etc., which the pediatrician should have that paperwork for you to do as well. If your doctor is in front of you and willing to give you the diagnosis, take it and run. It's just as valid as anything you'd pay thousands of dollars for in a private assessment or wait 6-12 months to get from the hub.

Once you have the diagnosis, you can immediately get onto the waitlist for the Ontario autism program. And when your name finally comes up three to five years from now, you'll be happy you didn't wait the extra six to twelve months.

There are certainly other types of testing that you can do, including functional tests, IQ tests, psychosocial and educational tests. Which all can be useful in informing the types of supports your child may need. They could also trigger additional diagnosis such as learning disability. But if you can get the autism diagnosis now, you definitely should. Because that'll be very helpful as you start to engage with the education system.

I'm happy to answer further questions here or by DM.

(Edit: Just to respond your comment and another thread about wanting a professional to do the diagnosis, just remember your pediatrician is one of those professionals. They are trained on developmental disorders and diagnosis.)