My thoughts are, If you need to ask this, you should just buy it.
If you are doing it to save money, you won't.
If you want to start wood working, its a good spot to start. Its a good excuse to buy tools. If you don't already have them, they will cost more than the bed itself.
Price a can of paint, some glue, dowels, screws, poplar at HD is a crazy price.
You don't save money building it yourself, and it will take a pile of time.
If you want to give something to your daughter that dad built then use that reason, not saving money.