If I want to know the isoelectric point of say rabbit IgG. Will all rabbit IgG irrespective of which antigen it generated for, have same isoelectric point.
Yes. All proteins including IgG antibodies have an isolelectric point; this a physicochemical property depending on aminoacid composition, size, and NOT DEPENDS ON ANTIBODY SPECIFICITY. Antibody active site determines specificity and it depends on very Little variability of aminoacid composition located on CDR1, CDR2 and CDR3.
Generally speaking, all IgG have close isoelectric points (somewhere around normal biological conditions of 7), since it is mostly dependent on their constant domains. However, it is possible to have novel antibodies, that might have extremely charged CDRs that might move the isoelectric further than 1 pH from the 7. It is highly unlikely though and if you are not interested in antibodies that could bind to something extremely charged (because that is the only way to get heavily charged CDRs), you can generally use normal conditions as isoelectric point.