USPS Postal offer both Medium $10.95 and also Large $13.95 Flat Priority Rates @> [URL removed]

How big is it? If it doesn’t weigh more than a pound with packing you can ship Priority for around $4.90 as long as the box isn’t too big.

Put it in a vacuum bag and shrink it before shipping it. UPS is better on Rates for large boxes over three pounds.

I would call them “Stuffed” toys.

Didn’t mean to be flippant. Too many variables
to give a succinct answer.

With USPS Parcel Post if one side is over 17" that can trigger a surcharge cost.
With Priority it depends on what “zone” you are sending to from your base…. and there the consideration is the length plus girth…
and all this is so confusingly spelled out on the usps.com site

A basic rule of thumb is that a Priority box will not be penalized if it is under 1728 cubic inches (which is 12 × 12 × 12″ or one cubic foot) so a box that is, say 8×8×16 is only 1024 cubic inches. A 10×4×20″ box would only be 800 cubic inches, 8×8×20″=1280 etc., etc..
This applies to your own boxing and to combining Priority boxes AND it only applies to items sent to Zones 5 thru 8 FROM you.

For closer locations [Zones 1 thru 4 FROM you] just be sure you don’t go over the Length x’s Girth of 84"

The Priority Shoe Box size might work very well for stuffed animals.

I have had good luck using Fed Ex Ground Home Delivery and sent some pretty big packages for a lot less than the USPS cost would have been.
You can get an exact quote [URL removed] [URL removed]

Be sure to enter that you will drop off at a Fed Ex location (includes Kinkos)and that you are using your own packaging and sending to a residence.

If it is a gargantuan State Fair type stuffed toy – try Greyhound. Seriously cheap. Only problem is the buyer has to pick it up at the Greyhound station at the other end.