Go to a pet store - there's a number of enzyme based products specifically for cat urine & other pet stains & odors, they really work.
Note - residue from other cleaners of Febreze may reduce the enzyme neutralizing (because the enzymes are actually "weakened" by working on other substances.) You may have to do two applications, and make sure it penetrates wherever the urine was.

Cat urine is terrible! Our cat got a urinary tract infection and peed a number of times on an oriental rug. It reeked. I had to wet it thoroughly, with the pet removal stuff, but now you can put your nose right up to it without detecting odor.

Since it is hand-made is it possible to replace the filler material thru a small hole? The filler will probably be where most of the odor is being retained. Also try a little baking soda and water mixed in a spray bottle. Spray on, then absorb back off.

carina has the right idea. The ONLY thing that will get rid of cat urine is an enzyme cleaner, any will do. (Nature's miracle, simple solution, bac-out, are examples, it must be an enzyme cleaner, and all will say they work on urine).
You must saturate all areas with enzyme cleaner where the urine got in the doll, and if you can, launder after treating (hand wash?). If you can't launder the doll, then saturate then let dry. It's OK to leave the cleaner in if you must.
I agree it may take a couple applications since you have tried other things, but it will work if you can get to where the urine is. Do not be deterred by the enzyme cleaner smell, that should go away, faster if you are able to launder.
Since you made the doll, perhaps you could replace the stuffing with new, and treat the exterior, thereby making sure you get to treat where the urine was. I know it seems drastic, but cat urine is nefarious stuff (no match for vinager, baking soda, or even bleach) and any trace left untreated by enzyme will persist. Just ask my comforter. :) (which must get this treatement once a year, sigh.)

I've followed your suggestions and think problem may be solved.I don't know why I didn't think to remove the stuffing.Right now I have a Bounce sheet stuffed in the head.When I replace the stuffing I'll wrap it around a new sheet.Maybe the baby will get a chance to play with the doll at last!Thanks for the help.I sure came to the right place. Gabriell

Thanks for posting, I was wondering how it worked out! :)

Just saturate it with white vinegar. That's what we recommend at the vet clinic where I work.

Since the vinegar has a smell I then would use a fabric freshener to get rid of the vinegar smell.