Draw a bunny head shape (or any animal you like!) on cardboard and cut it out. About 25cm tall works well, big enough to hold a decent haul of chocolate but small enough for little arms to carry. Use that as a template to make a second identical one. A curved bottom edge works really well for stability. You'll also need a thick cardboard rectangle to join the two shapes together and form the base of the basket. Double-wall corrugated cardboard is ideal because the basket needs to hold its shape once it's loaded up with eggs. MakeDo tools, cardboard scissors, or a Chompshop Chompsaw all work for cutting.
The trickiest bit is attaching the rectangle base between the two bunny shapes. Hot glue gives the strongest join (adults do this part if you're supporting younger kids), but MakeDo screws work realy well too and let kids do the construction themselves. You'll just need to have extra cardboard rectangles for the joins on the inside of the basket. Tape tends to pull away once there's any weight in the basket, so we avoid it for the structural joins.
Have paint sticks, stickers, collage materials, beads, and ribbon laid out for decorating. We use paint sticks rather than liquid paint for these because cardboard warps when it gets wet, and paint sticks dry instantly so artists can build, decorate, and take it home in one session. A MakeDo hole puncher is brilliant because artists can punch holes around the ears or along the edges and thread ribbon through, or pop in fresh flowers later.