A lot depends on what bike. sidecar combination you have. Suspension comes into play in a big way. Electric tilt could be a plus. A working antiswaybar would be a huige plus.
Load the outfit with passenger and dog and PRACTICE...THEN maybe reload a little differently with adding ballast or whatever and PRACTICE again. Practice easy at first and then work your way up past your comfort zone. Do this in a safe area and don't try to do too much too soon. DO not put ballast in th enose of the sidecar !!
Also as mentioned make sure your passeneger is aware of the lateral loads that are not experienced on a solo bike.