I guess I'm trying to simplify what I'll say.
To be honest the speech you've written is quite complicated for a novice speaker of Polish. You'd really need to write it down and read it which would be a bit much really especially as you'd be stumbling over the pronunciation. So I would suggest:
Wie Pan, kocham Kasią bardzo. Chciałbym prosić o rękę Pana/Państwa córki. Czy mogę?
That basically translates as "You know I love Kasia very much. I would like to ask for your daughter's hand. May I?" Pana if it's just him you're talking to, Państwa if it's the mother and father.
Then after the hugs and kisses etc and the tears of joy and the vodka, you can say "Jutro, zapytam ją" I will ask her tomorrow.
Now I'm not a native Polish speaker so there may be errors there or it may not be the 'correct' way but it'll do the job! Hope that helps. Good luck - let us know how it goes.