Worst case, you'll simply walk from T3 to T1, which is about 15 minutes. You might even not have to do that, as some Etihad flights go to T1. No visa, no collecting bags assuming that the whole flight is on one ticket.
You could go into the city, on a whirlwind tour. You'd obviously then have to get an on-the-spot tourist visa (depending on your nationality, of course) to leave airside / enter the country.