Three words for you: Jump on it! The difference in size alone would be worth it for a family of four. And you are far enough away from the anchor you should hardly notice it; and even if you do, you only have one, maybe two ports where you will drop anchor.
You are two decks above the Princess Theater so that is not an issue. I've never even heard any complaints from people directly above it.
And finally, Dolphin Deck is low enough that the ride on Dolphin/forward will probably be smoother than Baja/midship.
So take the mini and have a wonderful cruise.