We are investigating the SF in galaxies of the actively evolving Dorado group where signatures of interactions and merging events are revealed by optical and radio observations in both ETGs and LTGs. Our previous Ha+[NII] study, probing ~10 Myrs timescales, suggested that SF is still ongoing in ETGs. In this work, we use far-UV (FUV) imaging to map recent SF on times scales of about 100 Myrs. We used the Ultraviolet telescope UVIT on board Astrosat to image the Dorado backbone galaxies previously observed in Ha+[NII], with the far-UV filter FUV.CaF2 (1300-1800A). The sample includes NGC1536, NGC1546, NGC1549, [CMI2001]4136-01, NGC1553, IC2058, PGC75125,NGC1566, NGC1596 and NGC1602. FUV.CaF2 emission is revealed in all galaxies, tracing young stellar populations in rings and showing tidal distortions. The Sersic index, derived by fitting the luminosity profiles, is always n<3 suggesting that the FUV.CaF2 emission originates from a disk also in ETGs. The SFR ranges from 0.004+-0.001 M_sol yr^{-1} of [CMI2001]4136-01 to 2.455+-0.027 M_sol yr^{-1} of NGC 1566. Most of the recent SF is found at the periphery of the Dorado group where most of LTGs are located. For these galaxies, the ratio SFR_Ha/SFR_FUV.CaF2 is close to 1, except for the edge-on IC 2058, similarly to previously reported relations for Local Volume samples. For ETGs, however, SFR_Ha is about 15 times higher than SFR_FUV. The Dorado's ETGs define a separate locus in SFR_FUV, SFR_Ha space with respect to the LTGs, which is well represented by the relation log (SFR_FUV.CaF2) = 0.70xlog (SFR_{Ha})-1.26.The disk structure of the FUV.CaF2 emitting populations discovered in all the ETGs implies dissipative processes and wet merging events. The systematic discrepancy between SFRs derived from Ha and FUV fluxes suggests that rejuvenation episodes in ETGs cannot sustain constant SF over ~100 Myrs timescales.