Being impartial, as I haven't even seen your 1st coin...
1. I think it's a better idea to have it annually with a new date (as previously suggested) on each coin. (or biannually as the market dictates)
2. I don't think you should take nominations on breeds because of the vast amount of personal preferences there are out there, and we really don't want to forget any of our doggie friends just cause they are not as popular, nor an old breed. That 'drawing from a hat thing sounds fair', however it may be wise to incorporate every breed you can think of, not just the popular ones, and mixes too.
3. Since there are so many breeds (I don't know how long you will continue the series) the idea to put more than one on a coin should be considered.
4. I don't think any breed should be shown twice (thats just unfair!) unless you do something like a special commemorative one to remember some incident from the year. (In which the animal will be named)
By the way, what DOES #1 look like? And, are anymore available to buy?