It appears from the info you provided from the Honorable Discharge that Daniel was shipped overseas in January 1946, eight months after the hostilities ended.However, the 88th Division occupied portions of Italy until late '46, so this would be consistant with the info from his discharge.He was probably sent over as a replacement for those soldiers who had served enough time, and acquired enough points (points is a different discussion altogether!), to be sent home.
Regarding his medals: according to the Discharge, he was entitled to a WW2 Victory Medal.This medal was awarded to all members of the armed forces who served at least one day in federal service from 7 December 1941 to 31 December 1946.
The Army of Occupation Medal was awarded to members of the Army or Air Force who served 30 consecutive days in an area of occupation (Germany, Austria, Italy, Japan, or Korea). The qualification for Italy was 30 consecutive days anytime between 9 May 1945 and 15 September 1947.
Expect about a 6 month delay or longer to get the medals.However, since there were literally millions of WW2 Victory Medals issued, and probably hundreds of thousands of Occupation medals issued, you can find original WW2 era issued medals for sale for about $5-$10 each on places like EBay.