South facing garden - growing grass

Help!!

I’m meant to start building soon and have only really just learnt about orientation. Im reading so much that no grass will grow on the heavily shaded south facing lawn I’m going to have in a coastal Perth suburb. I hadn’t considered this at all and was just so happy to secure some land. I feel so sick thinking about it and just want to pull out of the whole thing. Half the reason I’m doing this is so my dogs had a small backyard to lounge around in and catch some rays.

Am I really out of luck? I can’t give them artificial lawn and paving would be so disappointing 🥺