I decided to knit a few plain bunnies with different yarns and needles, just for comparison purposes.

The first one is Drops big merino, an aran wt wool with 3.25mm needles. I found it was too thick and stiff on 3mm
The second is drops merino extra fine, a dk knit wool on 3.25mm needles. I had previously knit it on 3mm, but it came up a little smaller, and when I tried 3.25mm, the size was better and it is still not too open.
The third is drops muscat, a 100% mercerized cotton, and my usual go to bunny yarn.