Couple of things. It appears you have a Campbell Hausfeld, not a Kobalt compressor (CH does make compressors sold under the Kobalt brand). If the compressor is slow to build pressure it might be a bad head gasket or valve (valve plate). Both would be cheaper and easier to fix vs a new pump. Get a picture of the pump as well as any model numbers on the pump itself. CH used a similar family of inline twin cylinder pumps for many years. Parts are common.
If you decide you need to replace the pump I would suggest getting one of the Harbor Freight pumps. They are cheap and work. You want the "3hp" (or is it 3.7hp now) version. You need to make sure the motor doesn't spin the pump too fast or bog down under load. The motor will have a rated speed (something like 3450 rpm). The pump will also have a rated speed range. You need to side the motor pulley so the pump isn't going too fast or slow. Odds are good that the factory pulley is fine for the HF pump but you should check just in case. The HF pump might need new mounting holes drilled in the top plate and might need a new copper pipe from the pump to the tank check valve. None of this is too hard but fixing the original pump is likely your best option.
As others noted, the pump doesn't set the compressor's cut off pressure. That is the pressure switch. Since you aren't intending to change the switch you shouldn't have any issues with the new pump over pressurizing the tank. However, if your current cut out pressure is higher than the max pump pressure (the older HF pumps were only good to 145psi) then you may have to turn down the cut out pressure (done via adjustments to the pressure switch).
One of these might be the pump you have
Shop this 3 HP Campbell Hausfeld cast iron air compressor pump model VT4923/VT490000AV. Durable replacement pump for Speedaire, Husky, and Kobalt compressors.
compressor-source.com
Both are rated at 3hp (fine with your motor) but I wouldn't be surprised if the "3.7 hp" models used the same pump just run a bit harder.