Emirates airline from Cairo to Beijing and Asiana airline from Beijing to Busan.

No, you don't need to collect the luggage and reclaim them at PEK. It's international to international transfer in T3. The minimum transfer time is an hour. Thus your time is enough. Don't worry.
In addition, if your two airlines have luggage check through service, your luggage will be delivered to the destination directly. You can consult your airlines and confirm this information.