DS was tested for walnut allergy at our local hospital (referred to the allergy clinic by the GP) when he was about 3. It did involve a blood test, which the lady did very badly (unfortunately) - so badly that she had to do it a second time, by which point poor DS was semi hysterical, and I was pretending not to be!!
We were really, really unlucky that the blood test went so badly - DS still remembers it (he's 6 now), and was so upset by it that we haven't had him re-tested (which we were supposed to do when he was five). We are working on the assumption that he's still allergic (esp. following DH's fabbo idea of giving him a walnut to see what happened... what happened was that he was violently sick all over Betty's posh cafe in Harrogate!!)
I think we had to wait a few weeks for the results.
If I were re-testing him, I'd look into York Tests. I think they're around £200, but they're supposed to be very good, and involve - I think - a skin-prick test, which is much less traumatic.
It is of course possible that the testing procedure varies from region to region, and that your local hospital doesn't go in for doing full blood tests on children. It might be worth ringing in advance so you can prepare your DD?
If she is allergic, don't fear: it may just require vigilance. Allergies vary - in some people, it's just a kind of hayfever-y reaction; in others, it's much more serious. For us, it means warning hosts in advance that DS has a nut allergy, so that they know not to put his ham sandwiches next to the peanut butter ones! His school is also hyper-aware of nut allergies, and won't let children share snacks and so on.
Good luck with the test!