Hi D.,
Your such a girl after my own heart. I have done this in the past many times and have come across the same dilemma.
Well, so many have already suggested what I have done but here's my take on it.
My first thought was laundry basket based on expense. But I would buy it according to sex of child if you know what she is having. Like Blue, Pink, Yellow and definitely decorate it with ribbons. That would definitely make it fun and more decorative. A soft sided one is what I have for my son and I literally have it in his room by the door and use it as his hamper. I think I got it at Target.
When you give it to her you can say it's for the Baby's Laundry and maybe add and inexpensive box of "Dreft". Sometimes I have seen travel size boxes at Babies R'Us.
If you could afford a little more I have definitely used a cute bath tub or diaper bag.
If you do decide to just do a cute big gift bag but you want to change it up and still give it a fun "wow" effect. Buy a plastic rope (something to use like a Clothes Line) and some clothes pins (plastic or wooden) and pin everything you bought as best you can on the rope so when she pulls the rope out you can help her by holding one end (and have her hold the other end) and then pull everything out to display and hang like on a clothes line. Really fun and cute! I got the idea from a game I have played with the several showers I have given over the years and then I would just give them the clothes line with all I had hanging on it.
Have fun with all these ideas. I would love to know what you end up doing.
A.