When my Chihuahua puppy, Chloe, was in a terrible accident and needed emergency spinal reconstruction surgery the veterinarian gave us the choice between a $10,000 surgery bill and putting our new puppy down. Was it really a choice? After that I knew I wanted to start a charity that helped dogs who needed life-saving surgeries. That's when Paws for the Cause was born, and later it's annual #PawsGala dog fashion show.
Some people need time to warm up to a dog, and you should allow for a bonding period. However if your date is disrespectful to your commitment to your dog, i.e., encourages you to leave him or her alone overnight "because, she'll be ok, it's just one night, or a few more hours," I think this a bad sign.