I'm pretty sure, Marilyn, that at this time of year that filling station is open 24 hours.....I'm sure we've filled up in the past (in high season) before 7-00am.
I've also brimmed the tank with diesel in PP and the fuel gauge has never moved on the way to the airport. Fuel tanks take quite a lot of fuel after the pump clicks off - more than enough to get to the airport.
From previous experience, you are more likely to get to the airport and find the car hire cabin closed, and have to leave the keys in their key safe. If so, be sure to photograph the car all round before you leave it - just in case!
Hope it all goes smoothly for you.