Do you have options for a full-day gifted program or HG program in 1st grade (or earlier) where you're at? If not, I don't know that I'd bother testing quite yet - particularly since your dd seems to be happy. Part of the reason I wouldn't test quite yet is simply her age - I think if you can wait 1-2 years for a full IQ test (that you're paying for) you'll have less likelihood of dd possibly testing not quite as highly as she might due to simply maturity issues (paying attention, understanding it's important to answer the questions etc). You'll also have less likelihood of someone other than yourself questioning the results due to age at the time she was tested.
I also wouldn't pay for a full eval - I would only do that if my child was having challenges with school (which, oddly enough I've had with all three kids... so while I'm saying I wouldn't pay for an eval, that's coming from a parent who's kids have had full evals...)...
I also wouldn't worry too much about finding a gifted specialist, especially since you know and (I think) trust the previous tester. In an ideal world, of course I would want to have the evaluator be a person who specializes in gifted kids, but in my area, there are no such people, and it's worked out ok for us.
OTOH - I have to add that I've found that for my EG ds, having that # has been helpful. In his case, we tested early because there was a program that we were considering putting him in. Having the actual IQ # didn't really change anything about how we approached his education (other than issues relating to his 2e challenge)... but having the # *did* help us advocate for him at school, even when there wasn't a specific program etc that we were looking at that required a #. It was like having a little ace-in-our-pockets when we requested differentiation or more challenging work at school and our a teacher or school psych etc would try to pat us on the back and send us on our way thinking we were just another set of the "Every Parent Thinks Their Child is Gifted Gang" (apparently there is a large gang of these parents at our previous elementary school :D)... when we got remark (and we did, more than once in early elementary) it was just a bit fun to be able to show them that yes, indeed, we had #s to prove it
Best wishes,
polarbear
ps - fwiw, and totally OT, your description of your dd sounds *so* much like my dd who is now 8!