If I get a new Call of Duty CD for Xbox 360, will I have to restart my online multiplayer from level 1?

No you won't, the data is in your xbox 360, you can buy a new black ops cd and you'll be in the same spot as before, but be warned!, black ops is still about $60-$50. I suggest getting one used to save money :) It wouldn't be worth it to spend $120 dollars on just Black Ops, especially since MW3 is coming out in a few months.