Ilr - American passport holder

[Docrashmi]

My daughter has a American passport and on a dependent tier 1 general visa and she is 10 years old. I am planning to apply for ilr and then BC after a year. I have a Indian passport and tier 1 valid till 2016.

If we want to go for dual citizenship for my daughter, do I have to apply for her ilr?

If we don't want to go for dual citizenship, not apply for her ilr - what are the options for her to continue to stay here.

[Amber]

She needs ILR and one parent should be British/applying at the same time and the other parent be settled, I assume she wasn't born in the UK.