You would think that it would produce insoluble aluminum carbonate, but that isn't the case. Solutions of Al3+ are very acidic, too acidic for the carbonate to stay carbonate. Instead it will decompose to form CO2 gas.
2Al(NO3)3(aq) + 3K2CO3(aq) + 3H2O --> 2Al(OH)3(s) + 3CO2(g) + 6KNO3(aq)
The insoluble product is aluminum hydroxide. You should also see bubbles of CO2 gas.