Customer wants me to watch her dog at her house for just 8 hrs (Not overnight). Should I charge her hourly rate or Overnight rate?

Since it's not overnight, that would be a daycare rate. However, since it would be at her house, you have to consider if you want to offer that service, based on your availability & other commitments.. I noticed you don't promote daycare or overnight service - either at your place or the client's.

As Elizabeth mentioned, I think an hourly rate applies best in this situation. What I normally do is book this as a drop-in and adjust the cost to reflect the total based on the amount of time you'll be at their home. I personally charge $5/per additional 15 minutes, or $20/hour after the initial 30 minute drop-in time frame. I've never had an 8 hour stay, so you could always give some sort of discount; however, if they're expecting you to be at their home for that long, they also probably are aware that it would be at a premium price. You also could be missing out on other service requests while you're staying at her home, so that's something to take into account too, when you're coming up with a quote. *This would be a great chance for you to get your first Verified Stay review though!