Yes, anything that meets those measurements is great - whether it's a 5gal bucket, a big plant pot, a plastic container, etc. etc... You really can't go wrong as long as it is a solid color and meets those measurements. It could be a kitchen trashcan, even, as long as you can put 12" of sand/soil in there.
I use round plastic plant pots with the hole in the middle to drain excess water. I know Home Depot sells this size for about $2-4. Walmart will sell them for very little as well. Plastic storage containers are usually for sale for $2-4 as well in this size. Then pick up a bag of play sand or organic top soil from any store for under $4 as well. For about $8 you can make a proper laying bin and save yourself problems if she cannot lay.
Yes, you can drill a few small holes to drain excess water, but remember to only mix enough water so that it is moist but not wet. It's best if you pour the sand first and add water slowly, mixing, so you don't add too much.
Then she will know what to do with it. If it's moist enough and she has privacy, when she's ready she will go down and use it.