When we did Alice (using the LaGallienne text), we had the table on telescopic legs - so the table grew and got smaller, but Alice stayed the same. Along with some clever lighting, it really did look as if Alice shrank and grew.

I can't recommend the Le Gallienne script (samuel french) enough for the remarkable appendix in the back with directions for making the special effects in the play. It's pretty thorough and contains wonderfully clever ideas.

We did Alice a few years ago and did some "low budget, low tech" solutions. We had two identical doors behind our black traveler, one miniature and one full size. Alice would pull aside the curtain to reveal the appropriate door.
The table was a round piece of plywood on a mop handle and was held by our tallest student. He crouched down for the regular height and stood up and raised the mop handle to make the table "grow." (The bottle & key were held in place with hook & loop tape.) We had an extra long tube-shaped tablecloth that hid the techie as he stood.
Our front teaser was the same color as Alice's dress, so when Alice was huge, we made it look like the teaser was her hem. We had two legs cut out of muslin (ok, actually bedsheets) and painted to look like stockings and maryjanes and hung them from a batten. The actor stood behind the legs with a mic and did her lines. The audience loved the effect and my friend's little one still calls the play "the one with the legs."

Hope this helps.