IL you must be looking at a different IPL the one I get from Briggs show that a Primer, Choke, or Auto Choke carburetor was use on those 125K09 engines. On those the fuel bowl are aluminum therefore can not rust but can corrode thru in places from water.
So just randomly put a carburetor from another is a bad idea.
A couple things to check too are that intake tube has an o-ring on it between the carburetor and the intake tube. The thing is check the whole plastic intake tube for a crack. Plus when installing the new primer carburetor make it mates fully with the primer/air cleaner base. These are prone to warping from age, heat, and over-tightening.