I believe that the AS225r1 TCP/IP package (Might have come with the C= 2065 card) should be AmigaDOS 1.3 compatible. Good luck finding it, though. (If anyone has a copy, please let me know!)
Also, I think one of the very early AmiTCP versions ran on 1.3, as well.
Anyhow, you're in for a real adventure... These tools were not common, and networking wasn't very standardized back in the days of AmigaDOS 1.3. Sounds like fun! ;-)