This is handled perfectly in the first episode, not just in the above mentioned scene but in two others: when Lennie James' Morgan Jones can't move on until he puts his dead wife's walking corpse at peace, a task so Herculean it stymies him every time, and when Rick purposely seeks out a zombie he'd seen before, one in miserable, legless condition, in order to put it out of its misery. For a zombie epic, this is a remarkably humane story.
But it's still a zombie epic, which means there isn't much you haven't seen before. The first two episodes, at least, follow the familiar formula: our hero wakes up in hospital after a coma of indeterminate length to discover the world is empty and dangerous, starts looking for his wife and child whom he is certain survived the outbreak, meets up with other survivors who fill him in on the details, and butts heads the asshole who will surely destroy the survivors' fragile security and cause many deaths by his assholeness (here it's Michael Rooker as Merle Dixon, playing a redneck racist out of Casting 101). But so far the characters are compelling, the production values are outstanding, the scripts are above average and, perhaps the biggest reason I'm hooked, The Walking Dead understands that zombie epics are about putting all your personal bullshit aside and working together for the common good.
That's something all the gun-collecting survivalists who claim to know exactly how they'll survive a "real" zombie outbreak always forget. It's never the maniac who shoots at other survivors to keep them away from his stockpile who makes it to the end. It's the people who join together to help each other who do.