I think his concerns for protecting her were more to protect his soul fragment. Voldemort might be fond of Nagini, but he is completely incapable of feeling or understanding love, due to being conceived under the effects of a love potion. I can understand now why it is illegal to make such a potion.
That may be true, but because she is his Horcrux, he would still care as she would've been his last option for self resurrection or anything like that... it may not be a pure reason, but he still did care, even if for ulterior motives...