I kind of imagine this is a different character. I mean, where's her flour skin? Her sunglasses?
Her hat?
Supercalifragiliciousexpialidocious doesn't make her Gaiman's Death. Possibly an aspect or creation of Death--just as Dream makes nightmares and dreams to do his bidding on occasion. I mean, even DEATH can't be everywhere.
There are cells dying all the time, millions a second, right now. Is she there to collect them? I can imagine enormous events, like the deaths of solar systems, or galaxies, or segments of the multiverse are treated like maybe self-help seminar and she's the MC or a hot club and she's the bouncer. But for really mundane stuff? There's no way she could keep her sunny disposition, the poor lass would frazzle herself stupid.