Can't help with a Y2 list, but my DS was (is) a 'natural speller', and we've had two different approaches to this.
At his first school, the teacher gave him completely separate lists in Y1/Y2 on the grounds that there was no point in him re-visiting things he could spell in Reception. He got them all right, just because that's the way he is. I think it made a difference to him as it made him feel quite pleased with himself.
At his current school (he's now Y3), the words are laughably easy (to DS - some classmates struggle). At DS's request, I asked his teacher if she could give him some different spellings; she said she would give him some extra words that were related to their topic work (e.g. hieroglyphics), but that on the whole, she didn't see the point of giving a natural speller different spellings, as they would be able to spell them anyway without any effort (true). So you might find that no spellings really challenged your DD as much as you'd like. We try to catch DS out at mealtimes and so on with words like 'onomatopoeia', but he can just spell them.
Overall, I feel relieved that spellings aren't something we need to spend any time on at all at home. DS doesn't even look at them. Once your DD starts getting serious homework, you will be glad of her not needing to bother about spellings!
DD is in Y1, and she gets ten words a week which she has to work quite hard to learn. I don't know what the others in the class do.