When is it okay to omit a determiner? (as in "Everything for baby")

A friend and I walked past a poster advertising BabiesRUs and the slogan was "Everything for baby". My friend said it's bad grammar and should include "your" or make "baby" into "babies". I disagreed but couldn't give a reasonable explanation as to why it is okay to omit the determiner in this case, but I'm still convinced it's perfectly reasonable, especially because it's advertising copy and doesn't necessarily have to conform to strict grammar. But even in everyday English, it seems perfectly correct to me.

Is it okay to omit the determiner in some cases and what are those cases?

Like Evan said above, the advertising was deliberately using "baby" as a proper noun; and as such, it's not grammatically wrong. It's a common way for advertisers to play into the psychology of new parenthood (when your new baby is the 24/7 center of your world, it doesn't sound so strange to hear "baby" as a proper noun even from strangers and advertisers).

Consider a pet store advertising "everything for Fluffy" or "everything for Fido" - same exact principle, and it doesn't sound odd.