QNasal is a nasal steroid - just life Flonase, Nasonex, etc. Please note that this is NOT the same as a systemic steroid like prednisone (some people panic when they see the word steroid, but there are different kinds of steroids).
We don't use QNasal, but my son (age 6) uses flonase and it works great for him. It was prescribed by a pediatric allergist. We use 1/2 the adult dose. He has no side effects. He also mentioned QNasal to us - the mist is finer and it doesn't tend to drip like Flonase so easier for kids to use, but it wasn't covered by our insurance so we went with Flonase instead.
And your doctor's thinking is what I was also told: my OB had me use nasal steriods instead of claritin, etc, during pregnancy and nursing because it's local instead of systemic, and less likely to cause side effects.
From a pharmacologist point of view - what the note says is that they have not specifically tested it younger children. Nasal steroids have been widely tested and used in older kids and adults without side effects, so doctors assume that it will be ok for kids too - and at this point they have been prescribed for thousands of younger kids too. But since the company didn't SPECIFICALLY test in that age group, they can't list it.