That can't be done without manually setting the defect ID in project 2, and that will most have to be done through direct SQL queries. Then you'll have to also update all the history tables and attachment tables to use the new defect id instead of the old ID.
In short... I don't recommend you try this. There are too many things to screw up.
You should move forward under the assumption that the defect ID will have to change. To help the solution, you can create a new UDF in Project 1 and then run SQL to copy the bug id to that new column in the database. After you copy your bug to the new project (and you get the new bug id), you'll still be able to view the original id from project 1.
Sorry... there's just not a good solution for what you want to do. Good luck on your decision.
The only other potential fix I see it to use the QC API to access all your defects and dump the data locally to something like XML and download all the attachments. Then use the QC API again to recreate all the data in the new project based on the details you have pulled down. This would be a very intense process and require a lot of work. So I guess it boils down to how important it is to keep the same ID in the new project.