Hi C.,
I am a clinical psychologist (currently staying home now but practiced for a very long time).
If you find a child or clinical psychologist who will do the testing with your child, in most cases, it won't be just the IQ test but a full battery of tests. This will take a good deal of time, over several appointments, and it will cost a great deal. Insurance will most likely not cover the cost of testing in this case because there really isn't a significant presenting problem.
When I say there is not a significant presenting problem, what I mean is (unless I'm missing something) that a three year-old showing some trouble focusing during sports activities is pretty common, pretty expected, and unless he is showing other signs of difficulty in other areas where it is interfering with his day to day functioning or normal development, there is not much to really assess.
Most psychologists who do child assessment are so busy testing kids with developmental and cognitive delays and other serious behavioral issues that you may find you have a very long wait time. I don't know about your location, but in our area, a child with serious problems may be on a waiting list of one, two months or more for the best child psychologists and pediatric neuropsychologists.
The test you're speaking of is the "gold standard" when it comes to intelligence testing in the preschool set. Even though the test itself has a very long history with good reliability and validity, nearly all professionals recognize that the results in the preschool age category can be somewhat unreliable due to a variety of factors. So, it is unlikely that you'll find a reputable pscyh who will get you in quickly, give one test, and send you off with your IQ score.
Someone mentioned a mensa or on-line tests. These tests are not used for clinical or diagnostic purposes. Avoid them.
Talk to your pediatrician. Share your concerns and observations, and if necessary, he/she can make referrals to the psychologist.
Best to you and your son.
J. F.