If you are seeing struggles with phonics, you will want direct testing of phonological processing. The WIAT gets at some of the easy skills, but a child who is verbally gifted, especially so young, may well score quite high on those. So you want to make sure you assess complex phonological skills too, using something like the CTOPP. LD testing usually looks at a range of memory measures as well (e.g. WRAML), to look for deficits in retrieval and fluency, etc.
It's important to remember that achievement tests don't expect much of 6 year olds, especially when it comes to reading and writing, so it's quite possible for gifted abilities to completely mask any underlying LDs in something like the WIAT. It's also important to differentiate between what she can do, and whether she can do it with the ease and speed you would expect given her ability as measured by the WISC.
