Pumping for an older child?

I'm not looking for any "Ew that's weird" comments here so before I start please just back out if that's how you feel..

Ok so..

I'm exclusively breastfeeding my almost 6 week old, and I pumped a bit of milk for my 4 year old the other day because she's kinda feeling cruddy. Anyway, she's asking for more and I'm curious, is it really beneficial in small amounts? I mean how much would she need to benefit from the antibodies and is it really worth it to consider pumping for her thru cold and flu season?