Do you confirm a dog-boarding request when the dog owner has not committed to a meet and great?

Go with your gut. This owner does seem unreliable. A 10 week old puppy is going to be a handful of work and she knows it.

Message her that you won't be able to watch her puppy because a M&G is a requirement and there's no reason to feel bad about it.

If you do go ahead, make sure the booking is adjusted to reflect 3 full days of care (Friday, Saturday and Sunday) since Rover's system is only going to charge her for 2 nights. Remember, each night is good for up to 24 hours and her intended dropoff and pickup times exceed that amount signifcantly.

BTW, your rate is so low. Only $1 more as your puppy rate, seriously?

Full disclosure I have confirmed bookings before and likely will again but rarely and only for specific circumstances - one is if someone from out of town is visiting and wants day care or boarding near where they are visiting not near their home area, the other is if someone has a last-minute booking need (i.e. family emergency, last-minute work trip, or last-minute cancellation of another sitter). In these situations, I make sure to communicate a couple of times with the client and ask many questions about the dogs to ensure it is a good fit. In a situation like yours I would insist on the Meet & Greet b/c there's no reason one can't be made, even if it's the day before. Unless she has a very good response for why she seems so flaky I would politely let her know that you require a Meet & Greet prior and if she is unable to meet it is likely not a good fit. I know the instinct when you're new is to take whatever comes your way but trust me when I say it's better to do the Meet & Greets and go with your gut.