The Chronicles of Sheldon Mayer's Sugar & Spike
The Doggie That Wasn't!
Sugar & Spike #48 
Dedication: Lisa Ray (age 6 months), Vancouver, via her Aunt Rayline
Spike gets agitated when another baby won't let Spike play with his imaginary dog. This time it's Sugar's turn to try to be the reasonable one. That trick never works, so she changes tactics to try to get the other kid to admit there's no dog, and failing that, chases the imaginary dog away to solve the problem. Positively King Solomon in her wisdom. Unfortunately, Solomon didn't have to deal with baby logic, which in this case just creates an imaginary giraffe.
Great little story, demonstrating one of the common dynamics of the series, Spike being the more naive, gullible and imaginative one, and Sugar being the realist who finds herself with the job, if not the right temperament, of his protector.
Characters: Sugar, Spike, unnamed small baby
Property damage: Spike's suspenders
Sugar's treatment of Spike: overall protective, in her own way, but she does drag him around by said suspenders until they snap
"There's only one way to end this nonsense!"