The dates you see for “open” periods when you go to prepare a vat return will be the correct ones, as those are pulled by QuickFile from your HMRC account in real time. The deadline dates on the key filing page are probably based on what you’ve set as your quarter dates in your QuickFile settings.
Almost everything to do with VAT quarters talks about them in terms of the month ending, so March would mean the quarter Jan-Mar, whose deadline date is 7th May. But the QuickFile vat settings ask for the month starting, so if you set that to the option that mentions “March” then it means quarters of Dec-Feb and Mar-May. The Dec-Feb deadline would be 7th April…