I was having this problem frequently when I was typing with my WI-FI keyboard that I just purchased. It happened mostly when I was typing a note in email, it was so frustrating waiting for it to catch-up and then having to delete the double words, etc. I also noticed that my WI-FI mouse was acting all squirrelly, that at times it seemed to have a mind of its own.
Then I just happened to read an article about routers and how all of the WI-FI things we have in our homes (cell phones, TV, Kindle, computers, etc.) that it is a strain on an older router's capabilities. It said that the newer routers were better to handle all of these items. I googled routers and found that the Nighthawk 1900 from Netgear was a good router to get and it wasn't the most expensive to buy. I paid around $120 from Costco.
Since that time, I have not had any more problems with "delay" typing. It seems to me that to fix any problem, all you have to do is just throw money at it. Fortunately, I could afford this one problem, this one time.