Well, she doesn't look like a NZ Red in either her color or her type; she could be a very smutty red with poor rufus, and with a long body and ears. (She looks like she could be a Flemish cross to me). But the litter she had with a REW buck does not necessarily disqualify her from being a NZR.
I see 6 chestnuts (aka chestnut agouti) and three blacks in her litter, plus the REW that died.
A red is a chestnut agouti with two non-extension genes <ee>. If the REW buck did not carry non-extension <e>, their litter could definitely, in fact probably would, have chestnuts.
The gene that produces self black, <a>, is another recessive. If both the doe and the REW buck carry it - which they obviously do - you'll get blacks.
Judging by their litter, I'd conclude the doe is <AaB_CcD_ee> and the REW buck is <?aB_cc_D_E_> (The question mark in the buck's code indicates that he could have a dominant gene along with the recessive gene he gave to his kits, but we don't know for sure he isn't homozygous for that recessive.)