Hello and thanks for your question.
Did your daughter have any trauma to her eye or was she rubbing her eye, sneezing, or coughing today?
I think unless this is an astoundingly painful headache or she has other neurological signs such as listlessness or changes in vision, I think you are probably safe to wait until the morning to see her pediatrician. The burst blood vessel in her eye is a sign that there had been increased pressure transmitted to her eye, either through straining against a heavy load, rubbing the eye, coughing or sneezing, etcetera. It is very easy for a child to rub the eye while distracted with a headache and not realize it. It is essentially a bruise on the eye and should go away over a week or two.
When someone's blood volume depleted (they are dehydrated usually) it can be a contributing factor to a headache so she may benefit from hydrating herself.
So to sum things up, unless there are those signs you mentioned, or the ones I mentioned I think she's safe to wait until morning.
Does this information help address your concerns? Does this make sense? Do you have any other concerns that I haven't addressed?
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My opinion is solely informative and does not constitute a formal medical opinion or recommendation. For a formal medical opinion and/or recommendation you must see an eye doctor.