I agree that we can't force spirituality on our children and that they need the opportunity of choosing for themselves.  Fear of the unknown is hard to over come and no one likes to be forced into something, it usually brings resentment.  However, I think often in the church we let those excuses to get out of opportunities to grow.  She may not fall away from the church, but she will miss out on blessings.  I don't think that should be taken lightly.  The scriptures says when we do what Heavenly Father says, he is bound to bless us, but when we don't we have no promise.  Blessings come with obedience to the gospel, which often requires sacrifice on our part.  We should be doing everything we can to recieve blessings in our lives, instead of justifying ourselves in what we can do. 

Answering your question, I'd probably say, "it's your choice.  You don't have to go, but there are people waiting for the work to be done who really need it and want it.  Are you willing to deprive them of the blessings they have waited on for so long?  If you are then perhaps you should wait for..."  then remove  some 'blessing" or privilage that your daughter has been anticipating from you. 

I always remember  what the prophet Joseph Smith once said, paraphrasing, A religion that doesn't require the sacrifice of all things, doesn't have the power to save.  If we aren't willing to make that sacrifice, then can we be saved.  This gospel isn't a gospel of conveniance but The Gospel of Salvation, we need to treat it as such more in our lives.  There's my soap box for the day!

I have to agree with Kpat when it comes to forcing your daughter to go.  It should be a spiritual experience and that you can't force on a person.  You might remind her of the people who are waiting for the work to be done.  "I guess they can just keep waiting a little longer" you say with a small sigh of "oh well" in your voice.

Perhaps if she were taking your family names, your family members who are waiting, she might look pass the shyness.

This is really just my opinion of the matter.  If your daughter is not comfortable going with the group of youth than it would be pretty awesome in her eyes if she wasn't forced to go.  Maybe she needs to just go with you for the first few times.  My daughter will be turning 12 in July and we might have the same issues.  I wouldn't want to ever force things on her because I know by doing that it is taking "choice" away from her.  My two sons are turning 8 in August and I am making it very clear to them that it is their choice to be baptized.  My boys also said they didn't want anyone else there except for their family.  They don't like people looking at them and they don't like all the attention being focued on them.  So, that might be something that your daughter feels as well.  I can't imagine that your daughter would fall away because of not doing baptisims.  I think patience, understanding and long-suffering will go a long way than someone being told the "have" to go.  Again, this is just my opinion on how I would approach it.