OK - I come at this as someone who really believes in getting kids reading. I'm not one of those posters who thinks children should let a thousand flowers bloom until the age of 7. My DD1 is at the top of her class and my DD2 is in nursery and I've been teaching her her phonics since she got the hang of colours and shapes. I tell you this just to provide background on what I'm about to say.
You are fine. She is fine. Look here:
www.readingchest.co.uk/book-bands
for reassurance. Your DD has been learning for one term. You say she's made no progress - could she read when she started reception? Because if all she had were phonic sounds this is demonstrably untrue.
She should be sounding out unfamiliar words. That's how phonics decoding works. And if her book band is the right one, she should be able to read about 75-80% of the words - so she should be faltering a bit every other sentence. Otherwise she's not being pushed.
As for word recognition, of course there are some "tricky" words like "the" which just have to be taken on board. But in the main it is all about the phonics. When you say "as quickly as her peers", anyone in particular? I can't believe that after one term, that many people in the class are Stage 3 ORT.
The reading chest website above used to group the colours by academic year and it was notable then that reception was typically pink/red, Year 1 (sorry don't know Scottish equivalent) yellow/blue/green - and then Year 2 there was a huge range of colours they typically got through in a year. I think this is because reading really is a "penny drop" skill.
And I say this kindly - your stress about this isn't helping. You have to chill. If she feels your tension, she will not enjoy reading. It will not be her happy place. And you'll always have battles.
My advice is to get to the end of the Faraway Tree and then have bedtime stories which are just a bit harder than her current level and follow the words with your finger. She will absorb much more that way. And have a chat to the teacher about what to work on over the holidays if that's what you want to do - are there digraphs etc "ck" "ch" that she could work on?
Google also the reception keywords - you can get them as fridge magnets. Must go and do nursery pickup - good luck xx