If you show both of your tickets at check-in it shouldn't be an issue. I've never had a problem with this.
And if you do have to re-check, agree with B747 - 2H45M is *plenty* of time to check collect bags and check back in as long as you don't have to deal with visas. Key will be to take a taxi to T3...you can pay in currency other than UAE Dirhams without a problem.