How often is luggage transported to the wrong ship? Should I pack afew changes of clothes in the backpack we are going to carry onboard?

I would definitely pack something in a backpack. The odds of the airline losing your luggage are higher than the cruise ship.

I don't think you have to worry about the Conquest. Its the only Carnival ship in the port on sailing day. So if you are flying in, the carnival baggage guys really don't have a way to screw that up. But as Cruiseman said, the airlines are more likely to "lose" a bag, so bring a carry on with a swimsuit and a change of clothes and anything you may want right away as the luggage may not get to your cabin until 6 or 7 PM the first day.

If you are driving to the ship, the chances are zero because you drop you bags off in front of the ship you are getting on and there is no other palce for them to go...

When you get to the pier in Miami, if you have a few extra bucks, ask for the bag-handler "Big John." He will get your bag on the ship promptly and most importantly have your bags waiting on you when you get off the ship making it easy for you to get out of the area quick!