I don't know what you mean by "afraid of crowds," exactly. If you mean "I would prefer the park to not be crowded," then I think late September/early October will probably be OK. I imagine it will be somewhat busy, but not nearly as bad as a couple weeks later when fall breaks start kicking in. If you're used to very large crowds, it will feel fine, maybe even better than you're used to. If you're used to very low-level crowds, you may be a little disappointed. Either way, you will probably have at least one Halloween party date (that day will be quite busy and the park where the party is held--presumably
Disneyland--will close early). Weekdays should still be OK aside from party dates.
Now, if you mean "I will literally freak out if I am in a crowded situation" then that's different (and I'd say go in January in that case), but I don't
think that's what you're saying.
January may be too cold for your DD, especially at night. It is likely that at least a couple rides will be down for rehab, possibly major rides (and probably more than a couple rides across the two parks). Historically, at least a couple areas in the parks go under rehab at this time, so you'll be looking at construction walls in some places. There will be less entertainment. Yes, provided you go after the week of New Year's (or so), crowds should be quite low. I'm really wanting to try going at a low-season time such as that myself someday. But if you really want your best chance of seeing everything the parks have to offer, it's better to go at a busy time. If you're really planning to be in the parks for 6+ days, you should be able to see everything regardless of crowds.
The only other advantages I can think of for January is that Space Mountain will be regular Space Mountain instead of Ghost Galaxy. That's ALMOST a dealbreaker for me, but not quite. Haunted Mansion may be down in January, depending on your dates (it will be Haunted Mansion Holiday in late September/early October).
But since your DD is sensitive to the cold, I'd choose your October dates too,
unless you absolutely hate Halloween. There will be a lot of Halloween-ish decorations in late September/early October, so I imagine there are a few people who would get bothered by that.
(OK, I don't even like witches but I figured I'd never get to use that smiley again.) And if you hate Halloween then I don't think Haunted Mansion being down in January would bother you anyway.
Have a great trip, whenever you go!
