The Mechaber writes in 688:7 :
"If one is sailing at sea or going out in a caravan and does not find a Megillah to take with, one should read on the 13th or the 12th or the 11th without a blessing. And if it is impossible to wait until those days, there are those who say that it can be read even from the beginning of the month"
We see that according to some one can read the megilla even at the beginning of the month of adar when they will be traveling afar and won't be able to read from the megilla on the proper days.
When it says that from the "beginning of the month" can we extend this to the first month of Adar as well when it's a leap year ,and say that this is the zman as well?
The Mishna Berura (21) brings the passuk " and the month that was turned from grief to simcha" as a reason why we can technically read already from the first of Adar when no other choice. Would that passuk apply to Adar rishon?
On a side note, those opinions who say that there is simcha in adar rishon (Chasam Sofer ,Shevet Halevi..) may be a proof to say one can read in first adar when in a bind.