Hi Olivia,
Welcome to the Mattress UnderGround. Thank you for your question.
As far as mattress protectors go, Naturepedic, Avocado, Birch Living, and MattShield all offer organic cotton protectors with a thin TPU layer sandwiched between the cotton. There are also cotton covered, wool filled mattress pads/protectors that work really well too. Most of the TMU trusted members that offer organic products carry something similar; @TheCleanBedroom, @OrganicBedroom, @EthicalMattress @PlankAndCoil @Shepherds_Dream are among many here that offer great options for mattress protection options.
I personally use a wool filled protector and definitely sleep cooler with it. We use organic cotton protectors on our guest beds and no one has complained about comfort or feel yet. I used the Brooklyn Bedding Terry protector for a while too and thought it worked fine, but I ended up preferring the wool filled option overall.
As far as what to place the mattress on, the DLX is a pretty substantial mattress, so I would look at something like the @MattressFoundations Terra Bunkie, which is only 1.75" high, or their Terra Foundation, which is 5.5" high. One nice thing about those is that if you eventually move to a traditional bed frame, you can continue using the foundation with it.
I also picked up a Yawnder4 adjustable base for my mother-in-law to use with her @dlx premier hybrid, also a firm/med. It offers zero clearance, so it can sit directly on the floor without legs, or as low as 3" off the ground with the up to 12" leg segments included. That can also work with most traditional bed frames later on if your setup changes.
Hope this helps and best of luck with the new bed and sharing the bed with the little one.
Maverick