Welcome to disABILITIES.
The Guest Assistance Card (we abbreviate it as GAC on this board, to avoid typing so much) is not really meant to limit the wait in line (the text on the card even says that); it's more of a way to let CMs know what sorts of assistance someone needs if they have invisible disabilities. If you are using the wheelchair accesible/handicapped entrances, there is often a longer wait than just waiting in line.
Examples of some of the things a GAC might allow would be:
-allowing someone without a wheelchair to use the wheelchair accesible entrances (someone with a wheelchair or
ecv does not need a GAC to use the accessible entrances)
-allow a waiting place out of the sun when the "queue is in the sun for a considerable amount of time" for people with conditions that are affected by the sun or heat
-allow a stroller to be treated as a wheelchair
-allow a quieter place to wait for someone who can't tolerate waiting in line (like person with autism)
We haven't been to WDW in October, but have been in September and the lines were very short. In fact, DH and I went on an adults only trip in mid-July and found our waits then were very short - not what we expected. By using fastpass and going early in the day (with a 3 year old, you will probably be up early anyway), you should be able to see a lot with minimal waits. Dh and I went to MK one day just after opening and were able to ride almost everything in Fantasyland, HM, the Steamship and the Pirates before 11:30 without getting any fastpasses or doing much backtracking.
We use a GAC for our DD who has a wheelchair and has multiple disabilities. Even during Spring break, when it is very busy, we find we don't need to use the GAc very often. By using fastpass and planning, we are able to minimize our waits.
The rides that usually have long lines are the thrill rides (which my guess is you won't be going on much with a small child) and the Fantasyland rides. By going early, you should be able to get on a lot of those with short waits.