There are several reasons the waiting period for a fully trained service dog. One is dollars -- the training is expensive and lasts 12 to 18 months on average. Another reason is that the training agencies have to wait until any dog is old enough for their temperament and intellect can be assessed. Additionally, they will not place any dog that is not FULLY trained and they have had adequate time to work with taand train the handler.
Your pup, right now, is too immature to provide the services you may need, other than,of, course, the outstanding companionship and devotion. Doesn't mean he/she won't get there - just mean they aren' there now.
Your thinking is correct about training. Get into a basic obedience class and take it seriously. Then move to an intermediate training class. During that time you can ask around for trainers that do specialy training.
The next important item is - get a letter from your doctor/psychiatrist stating your need for a service dog. Keep that letter - it will open doors for you.
Many group/individuals who train service does are not familiar with toy breeds. Keep that in mind and realize it is not a handcap but may give you a few problems with finding an advanced trainer who is familiar with toy breeds.
Example: when my Yorkie got her/our scholarship to service dog school they were appalled when I showed up with this little dog. First, like I said they had a great deal of training experience but none with dogs this small and secondly I was dealing with a prejudice that they thought only they could chose a good service dog. True, they had much experience with that, but I had other reasons as well. She turned out to be the head of the class and trained at a rapid pace! Changed everyones mind!
There is a man in Texas who is very active in training dogs for the military folks. I'll try to find out his name -- of course, the waiting time may be too long as well.
Good luck. Your new best friend will be your greatest joy and at this early stage a bundle of overwhelming energy. Just got to get through that. Need to stay very positive with this pup -- that is VERY important.
Thank you for your service and glad you found your pup
