K.F.
I live i NYC, it is a very popular thing to do
You have to buy tickets ahead of time and you want to be on the first boat. It will be crowded, even more so in the summer.
As for the 3 yo, it depends on the child. I could not take my 2.5 year old, he would not sit on the boat ride and would have no interest in the statue or ellis island.
If you do go though, stop at ellis island, I think that is a better trip than the statue, it truly is amazing what those people went through