DXB's website says there are 24-hour free buses between T1 and T3 and between T2 and T3. You can also take the Metro between T1 and T3.
cdclean's QR flight will come into T1, but the KTM flight goes from T2. Since s/he has tons of time, getting from T1 to T3 and then from T3 to T2 should be possible with the free buses. Obviously, a taxi would be faster, but there doesn't seem to be much of a rush.