When I make baby quilts, I usually make two: one for "show" if they want it for that, and one to be drug around and thrown on the floor, taken outside, used to make forts with, etc....in general, played with and enjoyed. And I usually (but not always) make a pillowcase to place them in...just looks neater and supplies a place to store the quilt in if they don't use it now and again. And I tell the parents to use them both and enjoy them. If they wear out, I will make another (have to be careful about saying that now since I'm 72....:))...

Instead of wrapping, I often roll a quilt and tie a piece of the leftover (I always overcut!) binding around it as a kind of ribbon.

I think a pillowcase or tote, as suggested above, would be nice. I always wash my quilts first, they get dirty in the making, and to make sure all seams are going to hold up to washing. I do include washing instructions, but not detergent. As far as worrying about the care it will receive after given, that's out of your hands, once you decide to gift anything, then it's not yours anymore, so it will be cared for the way the recipient wants to. You are the one putting the work into making it, so you have to decide if they are "quiltworthy".

First Quilt as Gift
 

I LOVE tying the package up with selvage as a ribbon....maybe just even tying the quilt up with a selvage bow...not even put it in a box. My DH found my selvage supply and now every sleeping bag in the house is tied up with selvages.

If it bothers you that your careful planning and hard work may not be appreciated enough to get the care it deserves, I see nothing wrong with checking their baby registry and buying a gift. Not everyone has the point of reference to appreciate a quilt, and once you give it, its fate is no longer your business. Why knock yourself out? Or you could make a wall hanging type quilt for that baby's room. It will be less likely to get damaged. You will have to be careful that it fits in with the planned theme, if they have one.