Well, you have to know the Forster radius for the GFP-dye pair (can be
calculated from the spectra), but usually for dyes with good spectral
overlap, something <5nm should be good. A quick back of the envelope
calculation would mean (in solution) 1 rhodamine molecule (Rhodamine6G
should have good overlap with EGFP) per 50 cubic nm, or 2X10^22
molecules/liter, i.e. 30mM. The concentration of acceptor molecules thus
have to be very high. Self quenching also occurs by Forster transfer and
will happen, but you should see EGFP-Rhodamine transfer dominate at
appropriate concentrations.
Sudipta