I am doing my daughter's taxes for 2021. She moved to England in September to attend graduate school. Do I need to do anything special for this?

The main things to know: If she had income that requires her to file a tax return (if she earned income in England it would still be required to report it to the IRS or state if she meets the threshold).  Also, if she has foreign bank accounts, she may need to report (for example, if $10,000 an FBAR would need to be filed). 

Did she really "move to England" or is she just temporarily away from her home to attend school.  Is she still your dependent?

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html