what a lucky girl
At first, I misread it and I thought it said "I give my daughter to a cat" XD
So in Swedish do you always place the indirect object before the direct object?
For ditransitive, prepositionless verbs - yes.
What would be some examples of non-ditransitive and/or non-prepositionless exceptions?
Taking the sentence given here: jag ger en katt till min dotter is an example with a preposition. As for transitivity, it doesn't really make much sense with fewer than two objects, but with 3+ ones you can frequently switch around a fair bit.
How would you say "I gave my daughter a cat"?
Jag gav min dotter en katt.