I am installing a lawn irrigation system. I have an old irrigation pump 1 1/2 hp I picked up from an old system. I drove a 1 1/4" point down into a water table which started at 7 ft and I drove the point into it for an additional 8 feet. The well point is 36". The Well point is 8 feet into the water table as measured by the static water level in the point. My problem is I am only getting 10 Gallons per minute of water. I'm not sure if this is because of the size of the point, the amount of water available in the well (did I need to drive it deeper) or the capability of the pump. I was considering buying a new pump but I am afraid if the problem is the well I will get the same results. How can I check this?

Have you contacted the pump's manufacturer to see what the specs are for that pump? That might tell you if the pump is performing properly or not. It might be that 10 gpm from 10' or so down is about right.

I will do some research on the pumps specs and manufacturer. I would like to know if a 3' point 1 1/4 inch point is capable of providing more than 10 gpms,

Just bear one thing in mind. You are, I think, using a suction pump. It has only one pipe entering the well, probably just connected to the 1 1/4 inch driven pipe. Bear in mind that suction pumps will only work at depths up to about 25'. As you get deeper, the ability of the pump to "pull" water decreases. 7' feet is pretty good, but when you start pumping, the water level will drop as water is pumped, making your pump less efficient. You might simply be working against basic physics.