The Model Number is XXXXX
The Serial Number is XXXXX
It looks to be a Briggs and Stratto Engine and the number stamped on it is 123K02-0196-E1-02 ( I think)
The governor speed CAN be adjusted simply by bending the speed control arm backwards and putting more tension on the spring. The top speed should be about 3200 RPM. Here is the link to the parts list and the item number of the adjustable arm is #222. http://www.partstree.com/parts/?lc=briggs_and_stratton&mn=123K02-0196-E1&dn=50540004A You Do NOT need to buy a new mower as you suggested, you just needs to have the governor speed adjusted. A good shop should be able to do this for a bout $10.00 It would also be a good idea to have the mower tuned up at the same time.
Here is a link to the Briggs & Stratton 4-cycle L-head repair manual