I am always cautious about discussions of ADHD in 6 year olds, never mind highly-gifted ones. So many are struggling in environments that don't meet their needs, yet schools generally focus on fixing "bad behaviour", not a bad match with the child's environment. I would look hard at her classroom and schoolwork before assuming the child is the problem. Even without the added complication of giftedness, so many schools expect unreasonable amounts of sitting still and listening out of small children.
That said, I have 2 kids that do have inattentive ADHD (one mild, one extreme), and the signs were there when they were 6. When younger, though, it was more of a parenting challenging (getting them out the door or through a meal in less than an hour was always impossible). In school, attention didn't become a major issue until they were older, and LDs started to interfere with their schoolwork. When LDs make the work hard, sustaining attention on it becomes excruciatingly difficult. For my daughter, that happened young (grade 2-3), for my son, much later (in grade 6-7). Of course, too-easy work sets the inattention off big-time, too. Sometimes both at once (think math that is conceptually too easy to engage, but mechanically too hard to write out the lengthy show-your-work answers. Result - space cadet and a never-finished worksheet.) So the problem is not the LDs per se, but rather mismatched schoolwork more generally (whether too hard or too easy), rendering the work unengaging.
Keep in mind ADHD isn't an inability to pay attention, but rather an inability to *control* attention. ADHD makes it really hard to stay focused on things that aren't intrinsically motivating - which makes it look so very, very volitional. (Teacher: "I know she can pay attention when she tries - she does it fine with the stuff she likes! She just needs to try harder, and stop being lazy with the stuff that isn't as interesting to her.") With ADHD, the hardest thing in the world can be work that is too easy.
With respect to whether to test, it really depends on whether you see issues that are causing her real problems, now, or if it's just one teacher. If your daughter might be starting to see herself in any kind of negative way, or is acting stressed or resistant to any aspect of schoolwork (or other activities), don't wait. If you're worried that she is disappearing too much - or uncontrollably - into her own head, even when there's interesting stuff going on she wants to participate in, then that's worth investigating.
But if your daughter is happy, and it's just the teacher complaining that she's not paying enough attention to unengaging activities, well - focus on the environment, not the kid. Many gifted kids - especially those super-visual ones - have some pretty extraordinary stuff playing in their heads - rare is the classroom offering anything that can compete with its depth and richness. So while I tend to be a "more info is better" person, she's only six, and most testers won't do much at that age. If she's happy, and you can wait another year or two, you are likely to get more substantial info, especially if the issue isn't actually ADHD, or isn't only ADHD. However, if it's having negative effect on her now, don't wait. "Let's just wait and see if she grows out of it" is a terrible, destructive and pervasive educational myth.
Either way, every child can benefit from some explicit support and teaching of executive function skills. You can't hurt her by using resources like Smart but Scattered (Peg Dawson), acting as though ADHD were there, and helping build up her skills. You can do now what you would do if she actually were diagnosed - support and monitor - and if she needs more than that, then you can look at assessment and more intensive interventions.
The best diagnostic tool I think we have is - is she happy? Stress, resistance, or something that she can do but just feels way *harder* than it should for this child at this age - these are all big red flags that some barrier is in the way of the child doing what we are asking her to do. If you see any of those, investigating that barrier sooner is better than later.
