I heard that there is a move amongst paediatric gastro-enterologists, supported by Coeliac UK, to try to avoid endoscopies in children where possible. Presumably this would be in cases where there was a family history of coeliac disease or where the blood test results were pretty definitive.
When DD1 was diagnosed in 2006 (at age 2.8), she had an endoscopy which they said was pretty much a formality - the TTG levels in her blood test were pretty high. She had gas to go under - she sat on DH's lap while the anaesthetist just held the mask under her nose till she went floppy and then DH laid her on the bed.
When the DTs were diagnosed a few years later (they were nearly 4 by this time), I asked the paediatrician if they had to have the endoscopy to confirm their diagnosis, given the family history (DH's nephew had also been diagnosed coeliac in the meantime). At first he said they did have to, but eventually I spoke with the consultant paediatric gastro and he agreed it was unnecessary.
Unfortunately for your DD, blood tests to at annual check-ups seem to be the norm, so she may yet get used to the needles, but you may be able to avoid the GA/endoscopy for now.
As the others have said, it's pretty easy to get used to the g-f diet once you get started. I had been so worried about DD1 that to find all(!) I had to do was change her diet to get her healthy was such a relief - and within 2 weeks she was a changed child - boundless energy, no more awful constipation, vomiting or diarrhoea and she actually enjoyed her food for the first time ever!
Best of luck.