A.L.
Don't stress too much. Every baby/kid is different. I would at least consider a program outside of the house 1 or 2 days a week. I have my 13.5 month old enrolled in a program 2 days a week. She just started about 1 month ago. She wasn't really walking at the time. She was taking steps, but not really walking solo. Well after her first day at school, she was walking all over the place. Who knows it could have been a coincidence, but I think it was because she saw all of the other kids running/playing and walking! I was the same you are now. Worried that my daughter wasn't walking "on time".
I am blessed to have a great place close to my house. It's brand new, clean and the k1 program is still small so my daughter really gets good attention from the teachers.