I aplogize for not having read everyone's response, so if I repeat something that's already been said, forgive me.
I'm lucky that I have a husband (and in desperate situations) family, cousins, brothers,a sister-in-law, that would be more than willing to help should I need them. Of course we have livestock, along with the dogs, so our situation is different.
But, I can tell you, I've had a situation arise that made me stop and think about the mental well-being of my animals. Generally, I am wholly responsible for their care. It's not that my husband (or children) wouldn't willingly participate in their care, but the animals are my passion and I enjoy caring for them.
I got very sick a year or so ago. I have a form of recurring anemia, and my blood count had dropped significantly. I was sick for several days before going to the doctor who ordered a blood transfusion and then bed rest until I regained my strength. I spent two days in the hospital and during that time, we relied on my sister-in-law to care for the animals.
You wouldn't think two days away would be enough to cause such emotional trauma, but "my" dog, Greta didn't fare well. All the other animals seemed to go about their regular lives. Greta however, refused to eat, refused to leave the porch, wouldn't relieve herself, and acted extremely depressed. After I came back home, her depression did improve slightly, but she insisted on keeping a constant vigil at my bedside. She's stare at me, lick at me and whine.
I finally asked my husband to bring her food and water into the bedroom, where she'd take a bite, return to me, then take another bite, return to me. But she still refused to leave the room. My husband's attempts to force her out, led to her growling and snapping at him. Finally we resorted to my husband carrying me outside, and sitting me on the porch, so she'd leave the house. She'd go into the yard, just off the steps, do her business and right back to my side. This was a daily routine until I regained enough strength to walk out myself.
As I became stronger, her vigil lessened... she definitely could sense my being ill, and as I became stronger and healthier, she knew.
Lucikly, I've not had any major issues since then. I am careful to take my supplements and eat iron rich foods and am doing well.
But if I forget to take my medicine a couple days, or my iron starts getting low, she lets me know.
But it does make me wonder how she would fare, should something catastrophic happen. You think often about how it would affect your human family, but your pets often get over looked. That opened my eyes, for sure. My husband I decided that should something happen to me (which is not a pleasant conversation to have, but one that is necessary) that she will be put to rest. Neither of us could stand the thought of her suffering, and grieving herself to death.
There are people who aren't as lucky as I am. But there are pet sitters, dog walkers, kennels, who offer services to those who need them. If it's make you feel better, there's no reason why you couldn't call and discuss the "what if's" with them, to make sure they'd be able to accomodate you and your pup, "just in case."
Having a game plan is a necessity, when you have animals. I'm lucky that my sister-in-law, cousin and I have game plans in place should any of us need help.