ILR for child born in UK and travel out of UK without ILR

Hi,

I have been granted ILR on 23rd April 2014 and I have few queries regarding my daughter who is born in UK.
My daughter was born in UK on 26th Feb 2011 and her current visa status is Tier 2 ICT dependent with leave to remain till 3rd Jan 2015. I have the below queries.

1. Since my daughter is born in UK, please confirm whether I don't need to apply for ILR for her and can register her as a British citizen since I have now been granted an ILR.
2. I need to travel to Netherlands and then to India in the next month and can my daughter travel with me with her current visa?
3. Will there be any problems in registering as a British citizen for my daughter if she travels out of UK with the current visa?

Request your help with my queries and thanks a lot in advance

Regards,
Kiran