Yeah, but the Protostar was fast enough to get people to Earth while they were still a child! You make a fair point though.
She wasn't on the Protostar. She and her people vanished through a wormhole in "Counterpoint", presumably making their way to the Federation sometime in the ensuing few years.
Before you know it, some AQ politician will become popular by proposing a space wall, to keep those of the DQ out.... and make the DQ pay for it, too.
We already saw a bit of that in "Sanctuary". Only it wasn't the Federation doing it. The Federation puts out welcome mats. And once Bajor dealt with its own issues and managed to join the Federation, maybe they did too.