My daughter has turned 18. Do I just submit a new W-4 to my employer and can I do that at any time?

Yes, and yes.

Agreed!

However, just because your daughter is 18 does not mean you CANNOT claim her on yor return. The IRS allows you to claim a blood relative as long as you provide over half of their support and provided they do not earn more tha $3,300 (their personal exemption). That $3,300 figure is waived if the child is attending college or graduate school, up to their 25th birthday.