hi foxesocks
welcome to the forum
I must admit to being slightly torn on what to say-- on the one hand I am thinking best bet is to talk to your child's DSN for some assistance. They will have experience , your child's medical notes and will hopefully advise you sensibly.
On the other hand your thought on tweaking up the levemir dose is a very good one( that i agree with)
but........ normally basal testing should be done before making changes to the background insulin - but with a 2 year old that won't understand why they cant eat for a 5 hour period for a couple days in a row doesn't sound good for household harmony.
I think on balance ringing the DSN for advice is best bet