Sharing God with Children

My younger cousins are starting to get older now, the oldest will be 5 in about 3 weeks.  She is mighty curious and always asking questions.  Not only does she ask the questions but she wants in depth answers, not just the short ones we sometimes give children.  For a year now she has asked about my veil, "what is it?", "why do you wear it?". 

My dilema is that I know her parents do not believe and have told me before "we are not religious".  How much do I tell her? 

In other subjects, her mom is quite open with her.  My cousin asked what cremation was and her mom answered it.  I wasn't about to be the one who told a 4 year old about cremation...luckily her mom was there! 

But anyway, I digress.  I have told her what it is called, a veil.  But I have side-stepped the question of why I wear it in the past.  If she were to ask me again in the future now I would tell her it is something I believe in.  But I know then there would be "why do you believe in it?". 

Do I tell her why, saying it's in the Bible...which will only bring more questions?  Or I do brush it off? 

I would also love to be able to take her to Church with me one Sunday, but obviously that is up to her parents and I do not see them agreeing to that at this point at least. 

I think if it were not my little cousin, I would have no problem answering her questions because I do it all the time anyway.  But I do not want to step on my family's toes. 

Blessings in Christ,