Is the Greatschools.org ranking your main driver for wanting this change? I would never let a single source, especially a website where I don't really know who is behind it or exactly what data they are using, how old the data are, if the people behind the web site have any agenda of their own, etc., push me into a decision. It should be just one among many, many things you consider. You also mention that the school can "barely keep the children up to state standards" -- what is that based on? On Greatschools. org or on other data like state education reports? I'm not knocking Greatschools but I wouldn't rely on any one sole source if that's what's happening.
You have gotten good advice here about visiting the school and looking at more than a web site. I would add that you cannot necessarily go by the Gifted and Talented numbers. Find out more about how GT works in your district: Do kids get to move out of "base schools" to "GT center schools" at a certain grade? That would affect a school's number of students designated as GT. For instance, here, parents can opt at the end of second grade to move their child to a GT center school if the child tests into the program, so the base schools that these kids leave may end up with lower GT numbers; it does not necessarily mean the base school is a poor school, it could just mean that more parents at the school opted for the center.
Also, I don't fully get the idea of school transfers at will, based on the parents' perceptions that a school isn't challenging enough. If it's public school, usually it is very difficult to get a child transferred away from his or her designated, neighborhood base school unless there are pretty serious logistics and circumstances involved, such as, "My child care provider is in another area and we cannot transport my child from our designated school to child care, so we need our child to go to the school nearer child care." Other than those types of things, just saying "I don't like this school's poor ratings" may not be enough to get a transfer -- or it wouldn't be here; maybe you can make the argument there. I'm just saying, brace yourself to be told that your local school is the one you must use, short of some kind of extenuating circumstances.
Don't be afraid to go to a PTA meeting at the school your child would attend, listen in, talk to some parents afterward.