Sorry, but I strongly disagree. It's not your choice to make either. With "taking them with me" you mean killing them, which I find rather selfish and egoistic. I can understand the despair you must feel that there seemingly is no one to take care of them, but murder is not the way. Find someone that can love them as much as you do.
How do you think it is possible to find a good place for a pet so quickly? Let's say you found a good family for him. These people smile at you, you agree to visit them periodically while you are still alive to see how your pet is doing.
But then these nice people just won't open the door for you the first time you come. And you will never know what eventually happened to your pet.
But initially they were so happy that you give them your animal.
Someone may simply disagree with the fact that you have come to look at your pet.
And in the end, when a person has made the decision to die, he no longer has time to go to the family that sheltered your pet for months (if this family will allow you to come at all). And there is no time, because there are no moral or physical forces, because a person is dying. He's running out of resources
Another example: an animal that was taken into the family may be on the street in 3 months, in a year. But the people who took him into their family were so sweet and kind.
There are plenty of such stories.