For a moment i thought it said "my duck is eating [something] tasty" but then i readed properly and i found out it was actually "my duck tastes tasty" :(
Unless he has a sexual preference for ducks? I wonder? Could this be used to flirt? If i call a woman tasty? Hmmm or does that make me sound like I'm into eating people?
"moja" is for feminine nouns, "mój" for masculine nouns. They're both Nominative forms (used mostly for the subject of the sentence).
There's a full declension table of Polish possessive pronouns (mój, moja etc.) at https://en.wiktionary.org/wiki/Appendix:Polish_pronouns#Singular_subject:_m%C3%B3j (click on "declension of mój" to open the table).