The latter one might be Fredric Brown's "Blood" (text available here), but the attack on a young female (actually a literal bitch), and the revelation that the current era's people are plants, are separate.
In their time machine, Vron and Dreena, last two survivors of the race of vampires, fled into the future to escape annihilation. They held hands and consoled one another in their terror and their hunger.
In the twenty-second century mankind had found them out, had discovered that the legend of vampires living secretly among humans was not a legend at all, but fact.
There had been a pogrom that had found and killed every vampire but these two, who had already been working on a time machine and who had finished in time to escape in it.
Into the future, far enough into the future that the very word vampire would be forgotten so they could again live unsuspected--'-and from their loins regenerate their race.
"I'm hungry, Vron. Awfully hungry."
"I too, Dreena dear. We'll stop again soon."
They had stopped four times already and had narrowly escaped dying each time. They had not been forgotten. The last stop, half a million years back, had shown them a world gone to the dogs-quite literally: human beings were extinct and dogs had become Civilized and man-like. Still they had been recognized for what they were. They'd managed to feed once, on the blood of a tender young bitch, but then they'd been hounded back to their time machine and into 'flight again.
"Thanks for stopping," Dreena said. She sighed.
"Don't thank me," said Vron grimly. "This is the end of the line. We're out of fuel and we'll find none here-by now I radioactives will have turned to lead. We live here. . . or else. "
They went out to scout. "Look," said Dreena excitedly, pointing to something walking toward them. "A new creature! The dogs are gone and something else has taken over. And surely we're forgotten." The approaching creature was telepathic. "I have heard your thoughts," said a voice inside their brains. "You wonder whether we know 'vampires,' whatever they are. We do not."
Dreena clutched Vron's arm in ecstasy. "Freedom!" she murmured hungrily. "And food!"
"You also wonder," said the voice, "about my origin and evolution. All life today is vegetable." He bowed low to them. "I, a member of the dominant race, was once what you called a turnip."