I am traveling with my son on Singapore Airlines from San Francisco International Airport (SFO) to Singapore Changi Airport (SIN).
Does anybody know if they allow gate checking the stroller?
Yes. Most airlines, certainly all majors, such as Singapore, gate check strollers. They will also be returned at the gate on arrival.
To facilitate the process, see the Gate Agent beforehand so they can tag it. This will save time at boarding/pre-boarding.
Taking a child stroller/buggy is not at all uncommon but must also meet some practical requirements. It likely must be collapsible or foldable and under a certain weight. You really want it to fit through the belt scanner at the terminal entrance as well.
Unfortunately, SQ does not publish the specific requirements on their web site, few airlines do. If you are worried your stroller is too large, you can either call the airline to request the specific requirements or show the agent when you check your other bags. If it's too large, they will counter check it.
Since you have the stroller, also be sure you meet any child seat requirements: Child car seats and harnesses
Note, while SQ does not publish the specific requirements, there are a number of similar question out there indicating SQ accepts gate checked strolers just like every other significant carrier.