So she is 4.5 and in reception - one of the youngest in her class, presumably.
I have a feeling it's my fault since I do not practise at home with her, but I've noticed that she hates putting effort into reading or writing or math.
Are you saying that you are doing nothing at all with her? Most schools expect parents to do more or less daily reading with their child. I believe in many schools it is actually this daily practice 1-1 at home that helps a child learn to read, rather than the teaching of reading at school.
So if you haven't been practising at home at all, then I would think it is entirely possible that your DD is indeed 'behind', as in, other children in her class (who may be up to a year older, and have been reading at home daily) have started to blend and have generally been building stamina and fluency, whereas your DD perhaps isn't? And perhaps she is noticing this, which might in a feedback loop be contributing to her unwillingness to practise at home?
This is a tricky situation, in that putting pressure on her might make things worse. However what I'm saying is that you cannot rely on school providing enough practice for your child to learn to read without any practice at home. So if you choose not to make her practice at home, you need to be clear that this will probably mean that for a while, she will indeed be lagging behind those other children that ARE practising at home. Even 5 minutes a day makes a huge difference.
Personally I believe in letting children come to the 'academics' in their own time, and that pressure can be counterproductive especially at this age.
If you leave her to develop, just keep reading and talking to her, you can hope that she will then 'suddenly' click, and learn to read easily, without all the stress and pressure, when she is ready. This might be in a year, or in two years, or three. Perhaps she just needs to reach a certain developmental stage, perhaps she is just currently mentally preoccupied with all the other interesting things in her life and will come to reading eventually. But if you go down that route of 'zero pressure, won't make her practise if she doesn't feel like it, let her get to it in her own time' you need to accept that she might for a good while be 'behind' those other children that ARE practising regularly, with or without pressure. And you need to be vigilant that she doesn't learn to think that 'reading is not for me' (because sooner or later she WILL notice that 'everybody' else is reading and she isn't) and that she always knows that you believe in her and think highly of her, no matter her reading abilities. It can take quite some personal strength of convictions on your part, to 'allow' your child to 'fall behind', because you in effect disagree with the prevailing 'system' that expects all children to be ready to learn to read (etc) at age 4-5. So it is best if you do choose this, to do it consciously and be aware of potential fall-outs (eg on your child's confidence).
Alternatively (or in parallel) you can try sneaking in some regular practice at home without your DD realising. So e.g. step away from the school reading books but find games that you can play with her that practise phonemic awareness (I-Spy type of games), give her bath crayons and work it into writing letters/words during bath time, treasure hunts with single words that she can decode (if bothered) as clues, magnetic letters to play with and to write shopping lists with, etc. ... so she gets some practice but without realising it.
And/or you can try to find apps/digital games that practise/teach the things she is refusing to do in the 'traditional' homework way, and that she enjoys doing.