SOME parents of gifted kids tend to overinflate their kids. However, a fair number are aware of the multiple intelligences and multi-aging issues with kids who test high in at least some areas, and THOSE parents I find are pretty good about keeping perspective.
In other words, many ‘gifted’ kids (my son included) are gifted in some areas, average in others, and may even be below average in others. Intelligences are many, and the levels for each are often varied - every type of skill/understanding can be considered an intelligence, from social skills, to math, to language, to physical prowess, to culture even (acculturation capacity is considered an ‘intelligence’ officially).
I am not sure I agree with not telling her about what the tests are for - I wasn’t told myself, and I spent most of my life beating myself for being dumb, despite the evidence. So that won’t necessarily improve things. Sometimes there’s a problem with rational levels of self esteem no matter what path you take. PART of that tendency is related to the differences in how very bright people think (outside the box, ‘different’, etc.). It is the parent’s job not to just tell or not tell, but pay attention and tell if it is necessary. Not telling about the tests and/or the results is the default, however, until you see that 1) your child can appropriately handle it, and 2) he/she needs the info. And THEN, you have to help them digest the info, and understand that it imparts no VALUE (this being the flaw I see most often - being smart makes some kids ‘better’ according to their parents), but just different needs and abilities.
No matter which path she ends up on - ‘gifted’ program or regular schooling - the goal is a child who is able to function well in the world, understands and accepts herself, and is happy. It is hard to mess up if you keep that goal in mind.
As for whether to test, has she been in any gifted-type programs so far? Is she struggling with the pace or style of the current classes? Does she have a lot of frustration about school? If she’s having difficulty, then a change is indicated, so test to see if she can move on that way. If she WANTS to try the gifted program, again, go for it. And then add your opinion - is she being challenged? Is the style suitable for her? Will she benefit? Talk about it with her. From all that I’ve read, most people who are on the margin between gifted and not gifted benefit SOME by being in gifted programs, but do as well in regular programs PROVIDED they have some flexibility and opportunities for expanded work, in-depth projects, and variations in pacing. Not every program does that (most don’t), so if the school program is flexible, then it doesn’t matter which way she goes if she ends up on the margin. If the program is NOT flexible, then it will make more difference being in the gifted program.
Good luck!