you *really* should get a railing installed. that is a real safety hazard. your child is not going to climb on hands and knees for much longer and it is vital that you teach him to hold onto the railing once you start letting him go up and down that way.
my kids both were "early" on the stairs. we have a very steep staircase of wooden stairs. my daughter has falled down them before, when she was a toddler. it was horrifying. i was right there at the top next to her, and could not quite grab her when she started falling. luckily, she is very athletic and "knew" just how to log roll down and landed perfectly on her outstretched hands, protecting her face.
she was early going up the stairs, under a year. her brother was also. he is now 15 months and while i don't allow free roam (we have a fairly large house and i like to know where he is!) i do tolerate him going up alone, but i always remind him about going "the right way" and his sister, who is now 4 years old, i enourage to stay a few steps below him when he is coming downstairs if i can't be there myself, just as a precaution to break his fall if that were to happen.
she, as a 4 year old, and also as a 3 year old or whenever she started walking down the stairs, and any children who come over to play are *required* to hold onto the railing going downstairs. as an adult, i hold onto it too.
let me say it one more time and i'll shut up: get that railing installed pronto!!