Don't be nervous using small squares, just take your time, being careful of your scant 1/4 inch seam allowance.
A sharp needle plus VERY careful pressing is also important.
I've done log cabin blocks using 1inch strips and also 9 patch blocks using 1 inch individual squares and they come out great! Once you get used to working with small squares the regular sizes will look huge to you!
QuiltE----your cow quilt is awesome!!!