I'm going to throw out another option. A custom-wrapped rod. Northfork Composites, which became Gary Loomis' venture after selling his G. Loomis company to Shimano many years ago, is having their crazy-good annual Black Friday sale ongoing. Many blanks are $79 with code "NFC79". The Gamma Alpha and Gamma Beta blanks are $115 with code "BFAIR", plus $10 federal tax.
I have two rods on Gamma Alpha blanks (smooth, powerful, medium-fast) and one rod on a Gamma Beta blank (rocket launcher). I haven't cast all of the latest and greatest fly rods, but these blanks generally have a reputation of favorably going toe-to-toe with the finest and costliest rods in the industry.
If you want the rod in time for Christmas, this is probably not a workable option. However, if you can put a picture of the blank in a Christmas card, along with the name of a rod-builder of your choosing, the completed rod would likely be available by late winter/early spring. One nice thing is that your daughter will be able to pick out the rod thread colors and design, reel seat design, custom inlays, etc.
Considering the cost of these blanks, you should be able to have a rod built with top-tier components and be at or near your $400 price point.
I have had my rods wrapped by Bigdady Rods located in Pottsville, PA. Randy's work is outstanding, and I highly recommend him. Depending on where you live, you might be able to find a reputable builder closer to you. Dream Weaver Custom Fishing Rods is a builder located in Elizabethtown. I have not used their services, but I've heard they are very good.
Here is a link to the NFC website. The website is not very user friendly, but if you get to the main page and choose "Fly", you should be able to scroll around and view the various blanks. You can also download a catalogue where you will find more detailed descriptions. Or, if you call, you can usually get someone on the phone who is very knowledgeable about their blanks to help you decide.
Northfork Composites