I would guess that a 1/4 size will be too big. DS is an average sized 8 year old and will soon be moving into a 12" viola which is equivalent to a 1/2 size violin (right now he is in an 11" / 1/4 size). When he was measured at an older 6 he needed a 1/8.
There is a 3 year old in my DS's violin group class and she uses a 1/32 violin, the smallest available (from what I hear). My son was 10 when he moved up from 1/4 to a 1/2 size violin. I think there's no way your 3 year old will use a 1/4 violin for a while.
I started when I was 3 1/2 and I am pretty sure that my first was a 1/8 size but I was very tall and gangly and the determining factor is arm length. I could have had a 1/16th though... I will ask my mom. A 1/4 will be too large for a 3 year old though for sure.