(Am ex-primary teacher and mum of 2 - not that that makes me a total expert, nothing does!!)
I'd take a step back if I were you. Read to her loads, there are so many beautiful and funny books out there. Or things you loved reading and hearing at her age. Then leave them in her room or somewhere accessible for her to look at them herself without pressure. Also great events at local libraries, literary festivals, etc. Ignite her passion and hunger for it..
At her stage, so much of her day is controlled and organised by the adults around her, and so much of how she's judged is linked to how good a reader she is.
She's probably doing quite enough between 9 and 3 - reading is linked to almost everything at school!!!
Why don't you just see your role as linked to her literature immersion, so that if she's reading anything it's in a practical context? (e.g. recipes, food labels when shopping, signposts and navigation when walking/driving etc, etc). These are things her teacher will never be in a position to do.
I say do the formalised 'sit down with a READING book' (ugh) thing at school, home is for a rest, and for doing fun and interesting and more creative things. Think of it from her point of view.
Girls are under tremendous expectation to be fluent readers at a very early age, as it's traditionally been the way. Of course, all barriers to fluent reading like eye tests, etc should be monitored by the school.
And please stop worrying! I know you're trying to help, but when children 'click' with something it's just jaw-dropping how quickly they can progress. However, if you put her off by pressurising her, she'll never want to do it. And who can blame her..