Whenever we had a vaccination we always waited for any reaction before doubling such as a high temp.  There never seemed to be a problem for us and we never had to give double cortisol.  I gave pamol once because he was a little crabby after.  Each child will take the vaccine differently though.  If they get a temp it you can be sure their cortisol levels would rise normally in response, so that is what you would want to mimick if that happnes.  In that situation it is probably needed and therefore doubling would not dampen immune response. 

I think that that happens when you have been on steroids a long time at higher doses than at the smaller doses we give our kids or when doubling etc.  I would not give increased doses or pamol unless there was a temp problem though.  Keep checking the temp and go by how the child is for the next 2 days.