My dad and I play a day-by-day gome, where each of makes a move once a day. Does anybody else do this?

try DragonGoServer, or OGS

These are both good suggestions. If you need a link - http://www.dragongoserver.net/ or http://www.online-go.com/ . In general what you are looking for is called a "Turn-based server" there's even a whole subforum for them here on L19.

Do be aware though that your strength will change a lot if you are still improving if you play a game like that . I had some pretty silly people on one site recently accuse me of cheating for having won all my games there - it's not my fault I'm more competent than staying at 13k or whatever for the 6 months a game lasts... Quite amusingly I have a game going on one site at the moment where an 8k is giving me 5 stones - he deliberately lets his time go down to basically 0 before every single move (he has 600 games in progress or something ridiculous and our game started with 90 days each) so I don't really feel bad about him dying on basically the entire board now ...