First off, you are on the wrong side. You are not going through your firewall, which is the first line of protection for any DOS attack. And most routers aren't going to let icmp ping echo into their protected hosts unless you muck around with the firewall.
Second. if you look at the ping code, there are several timers. Since ping is not streamed, those timers allow it to wait for a response. You would need to change the code to have it not wait or to send corrupt packets.
Third, as everyone has said DDOS is distributed. You would need to enlist several attackers sending back to your router "valid" requests that flood it. That is what makes it insidious, that the packets aren't attributable to any particular source AND that the packets can look valid individually. They can also be designed to take up resources and that is what brings down a router.
How large are the packets that you are sending? Just pinging it a bunch of times normally isn't enough to fully bring down the router. I don't really know much about macs but I know with Kali and hping3 you can set the amount of times you ping the site and then how large the packets are. But it could just be that what you are doing is not enough to bring it down as well.
LOL, you need to look up what DDoS means. You're failing because you're missing hundreds if not 1000's of other connections doing the same thing.
That is not DDoS if it is just initiated from one point, it is just DoS, unlikely to be effective. What was your question?