Okay. There are some late 20th century alternative meanings, limited to the USA, e.g. 'absurd or ridiculous' and 'to swindle or deceive'.
This little phrase is a variant of okay. It is 20th century American and first appears in print in a 1932 edition of American Speech.
There are several alternative spellings - okay-doke, okey-doke, okee-doke, etc. In addition to these is the comic version that has brought the phrase back to popular attention in recent years - The Simpson's Ned Flanders' 'okely-dokely'.
All of them are just a perky reduplicated variants of okay, utilizing that favourite device of two-word phrases - rhyming. As a reduplication it is properly spelled with a hyphen, although it is often given without.
Like okay, 'okey-doke' is used to indicate that all is well, e.g. 'everything is okay here', but may be used when responding positively to a request. That is exemplified in this piece from Colin MacInnes' book City of Spades, 1957:
"One Guinness stout, right, I thank you, okey-doke, here it is."
See other reduplicated phrases.