Hi, and welcome to the forum 🙂
Sorry to hear about your daughter's diagnosis and needlephobia. There are a couple of things which might help a bit. Firstly, you could get a "Penmate" - this is a simple device which attaches to the insulin pen and is spring-loaded. It hides the needle from view - you place the end of the device against your injection site and just press a button to fire the injection in. Another option is to use an Insuflon cannula (you would need to ask your DSN or GP to source these for you - we used to get them through my son's hospital team when he was on multiple injections). With Insuflon, you would insert a short Teflon cannula (inserted with a needle that is then withdrawn and disposed of) - this cannula can be left in place for about a week (in any of your normal injection sites). It has a tiny "bung" which sits on top of the skin surface, and into which you would insert your injection pen every time you need to inject. This is suitable for one type of insulin only (ie only novorapid or only novomix - if your daughter moved on to multiple daily injections, she could inject all novorapid through an insuflon cannula, but would have to inject her basal insulin separately).
Your daughter's hospital clinic team should have a psychologist attached, and it may help her to have a session with the psychologist to find out about any help or techniques she could use to try and overcome her phobia.
For general type 1 advice, you can't beat this book: Type 1 Diabetes in Children, Adolescents and Young People, by Ragnar Hanas.
I hope things improve soon for her - a type 1 diagnosis is a massive shock and turns your life upside down, but it needn't be the end of the world 🙂