If it happens to be raining tomorrow, I'll postpone departure until the next clear day.
Literal
By-chance tomorrow rain [copula-だったら], next sunny day [until-まで] departure [object-を] postpone.
だったら is the conditional form of the copula だ — 'if it is X.' Used when the protasis is a noun or na-adjective predicate. までに vs まで distinction: まで alone ('until') marks duration up to a point, while までに ('by') marks a deadline. Here it's まで ('delay until').