Would your district accept WISC-V scores if you had your DD tested by a psychologist outside of school? Our district (and most in our area) will only accept the WISC-V for gifted program admission. Cogat not accepted.
If your DD had a WISC score of 130+, you could definitely make your case for gifted services. (Our district is now up to 134+ for gifted program admission, which I personally believe excludes some DCs who do need those differentiation services.)
And speaking as a parent w/DCs who apparently do not demonstrate many "characteristics of the gifted" at school - until a WISC is finally administered - I'm here to say that I'd go for outside testing if you can. I have been there/done that/got the T-shirt(s). Even if your district will not accept an outside WISC-V score, at least you'll have additional info to advocate for your DD w/teachers on an individual basis.
Good luck!