Pay before the due date. If you're paying online, make sure to setup your accounts first. Do a test payment to ensure everything will work smoothly.
It looks like your daughter's monthly due date will be the 17th and her statement date will be the 20th. If she wishes to control her reported balance, she should make a payment no later than the 19th. Capital One has occasionally surprised me and closed by the morning of the usual statement date.
The trick to pulling this off is to not have charges post right around closing. That means suspending use of the card three or four days before the statement cuts. As she starts charging at familiar merchants and learns how long it takes for charges to post, she can cut things a little closer.
If this is her only card and the limit is low, her reported balance won't matter a lot in the short term. Capital One would be the only lender looking at her report, and the thing that impresses them the most is pay-in-full behavior. When she's considering applying for another card, she should keep this balance down. 28% will be looked upon favorably. 8% is better.
From a scoring standpoint, keep in mind that both overall utilization and individual card utilization are counted. Individual card utilization is determined by the card with the highest utilization. With a single card, both of these factors are hit as one's balance rises. And one is hit quickly when the limit is low.
@Anonymous mentions a card's highest balance. Some feel that it's impressive that when this number shows that the card sees substantial use. Some cards like AMEX will use the highest statement balance to fill this field. The card holder has to decide whether a temporary scoring hit is worth showing a substantial highest balance.
Capital One reports the highest balance anywhere in the cycle. So you can have your cake and eat it too by allowing a higher balance mid-cycle while still letting a low statement balance determine utilization. I'd let this aspect take care of itself. The priority should be to free up her limit to have room to charge more stuff, provided that she can afford to pay for the stuff. 