First of all, the stories that we are so familiar with as a part of the "Alice books," were originally thought up as a sort of rambling stream of consciousness, told to three little girls by the Reverend Charles Lutwidge Dodgson as they enjoyed a leisurely boat ride one day along the river Thames. The three young girls were daughters of Dodgson's friend, Henry George Liddell, the Vice-Chancellor of Oxford University, Dean of Christ Church, and headmaster of Westminster School. Nearly all of the places and characters in the Alice stories are thought to have been inspired by actual places and people whom the girls were familiar with in real life. In fact, some of the places can be traced to actual buildings which still stand today.
As the story goes, one of the daughters, young Alice Liddell, enjoyed the stories so much that she asked Dodgson if he would write them down. It took him two years to do so, but he eventually finished the first book and published it under the pen name Lewis Carroll.
Those are the facts.... As far as my opinion goes....
I'd say that it's unlikely that Dodgson was accustomed to using any potent psychedelic drugs, as they were not very popular or readily available at the time of his writings. It is possible that Dodgson may have enjoyed absinthe, a spirit thought to posses psychedelic properties, but it's hard to say. Dodgson was known to be friends with members of the pre-Raphaelites, (a group of artists during the mid 1800's,) and absinthe was most popular among those types of "bohemian" groups. However, absinthe became most popular near the end of the 19th century, and the Alice book were published mid century. Furthermore, the psychoactive properties of absinthe, beyond those of other spirits, are thought to be highly exaggerated.
More common drugs during the Victorian period included alcohol and opiates. Laudanum, a mixture of opiates and alcohol, was a common household item during the Victorian era, and its my understanding that use of this "tonic" often led to more serious drug use and addiction. However, I really have no clue if Dodgson would have been the type of person to get high on laudanum or opium while rowing a close friend's children down a river in a tiny boat.
I think it's rather possible that Dodgson (Carroll,) used psychoactive drugs at some point in his life, but to say that the Alice books are specifically about drug use is far fetched. Inspired by them, perhaps, but not based on them. Dodgson was known for being extremely intelligent in mathematics, logic, and language. I think that the most likely explanation for the lively fantasy in the Alice books is Dodgson's uniques blend of natural talents. The Alice books often turn logic on it's head and do so in the flowery prose common in Victorian writing. I also imagine that the children themselves had a hand in contributing to the story. (If you've ever had the pleasure of making up a story while telling it it to a youngster, you know how that goes.) Children are connected to their subconscious in a way that most adults are not. They don't need drugs to come up with amazing and ridiculous stories, especially not when working with a creative genius like Lewis Carroll.
I thought this was an interesting question because I think that it deals with a common misconception. I took some time and looked stuff up because I wanted to know more about the answer. I knew enough about Victorian children's literature, the story behind the writing of Alice in Wonderland, and Victorian society in general, to know what to research online. I used Wikipedia and other online sources. I hope this information was helpful, and that my opinion at least seems well informed. I enjoyed learnign more about this.