You will need a VERY sharp small knife. Be extra careful while you are carving. The idea is to cut the vegetables, not yourself nor anyone else. I often use small "hobby" knife (Xacto) with razor sharp disposable blades that I got in a hobby store

Start with the carrot. You want a conical portion that matches the diameter of the top end of the squash. Carve a flat "bill" or carefully split it to open the "mouth".

Two flat slices of carrot can now be fashioned into "feet". This is a "cartoon character so actual shape isn't terribly important.

Moving on to the squash, remove a slice from each side. Shape the slice into a stubby "wing".

Next cut a small portion from the top end to form a flat spot to connect the "bill" to.

Use toothpicks to attach the various body parts. An alternative on the "wings" is to cut a slot into the body and allow the wings to stick out at a 90 angle from the body.

A pair of clove "eyes" complete the critter.

If these (or other similar vegetable creatures) don't sit out too long they can be used after the event in a vegetable stock so they aren't wasted.

This is ONLY a guide to get you started on the idea. Play with this a bit and have fun seeing your own creations magically appear.