Hi Kathie_K, welcome!
There are of course no "right" answers as to whether one should have their child tested if not absolutely necessary. But I personally think that if you will attain some benefits from it and it won't be unduly hard on the child, then go for it. In your case, it sounds like their are some classes that your child could attend. You are lucky to be in an area where there are classes for such young gifties - most classes requiring certain test scores seem to start around elementary school age for kids around here. Also, our son wouldn't have gone to anything at that young age if he couldn't also be hanging on to my leg.
You may want to consider testing before age 5 if there's a possibility that early entrance to kindergarten would be good for your kiddo. In many ways it's easier to start early than to skip later. In our personal situation, we had our son tested at age 4 so we could have results to bring to the school for a possible early start of kindergarten. We ended up choosing to skip 1st instead, which worked out OK.
There are also some drawbacks to testing very early; optimal testing is sometimes said to be around 7 or 8. Others who know more about testing can comment more on that.