Most airlines don't include pushchairs/prams/buggies in your allowance, they are free if you like. As for the 10kg I can't say, I'd give the airline a call and ask them because as you say you don't want to get there and have to end up paying excess.
If it's on the ticket I'd be inclined to think that you do have the 10kg though as it says it there in black and white
