0 can only appear once, since no digit that is included in the autonumerogram will appear 0 times. So our number must include "10".
Then 1 appears at least twice in the autonumerogram, so it must include a digit that is at least 2. If there are exactly 2 1's and exactly 2 2's, then 2 appears at least 3 times, a contradiction. So the largest digit in the autonumerogram must be at least 3.
If we want the largest digit to be 3, then the number is of the form 10A1B2C3 (possibly with some sections rearranged), where A, B, and C are all 1, 2, or 3. We must have A+B+C=7 to make the total correct, so either they are 2, 2, 3 or they are 1, 3, 3.
If A, B, and C are 2, 2, and 3, then there are a total of 2 1's, 3 2's, and 2 3's. The smallest number for these is 10212332.
If A, B, and C are 1, 3, and 3, then there are a total of 3 1's, 1 2, and 3 3's. The smallest number for these is 10123133.
So the smallest pan-digit autonumerogram is 10123133.