I'm 5'3" tall and ride an XS size gravel bike. I have only 9 cm of seatpost between the saddle and the frame, and you can see there's no possibility of extending that! I find the aluminium frame quite harsh and would like to swap my normal seatpost for a suspension one. Is 9 cm enough room for this to work?
As Daniel R Hicks says, it depends on the seatpost.
There are some seatposts that offer "passive" suspension—they have no suspension mechanism, and rely on the flexibility engineered into the seatpost's materials (always carbon fiber, AFAICT). From what I've read, these don't do much good. The suspension effect with these will depend on the amount of seatpost sticking out (more material to flex), so even if they do work, they won't work as well for you.
There are a few "active" seatposts that do have suspension mechanisms. Cane Creek has one where the mechanism occupies 70 mm of seatpost length, so that should fit. Redshift sells one that is bang-on at 90 mm maximum insertion depth.
I briefly stated this in comments on Adam's answer, but do be careful of where you are measuring from and to.
Seatpost lengths are usually measured from the bottom of the post to the center of the clamp. Redshift's website specifies that at its maximum insertion depth will leave 90mm from the top of the seat clamp to the center of the rails. It's not clear if you mean that you have 90mm from the seatpost clamp to the center of the saddle rails, or 90mm to the top of the saddle (remember that saddles can vary in height). Hopefully you meant the former.
Adam mentioned the Cane Creek seatpost. By my reading, the 27.2mm post is 345mm long, and all sizes have a maximum insertion depth of 274mm. At that maximum depth, that should give a minimum of 70mm of exposed seatpost. So the Cane Creek post may work for you and the Redshift post may not. (NB: if your seat tube isn't 27.2mm, be aware that you can use a shim to enable it to take a 27.2mm seapost.) I'm not currently aware of other brands of suspension seapost.
If not for suspension seatposts, it may be worth asking what tire pressure you are running. Especially if you have a tubeless setup, big tires can take surprisingly low pressure, and the tires provide a surprising amount of suspension. At 135 lbs of rider weight, I run just under 40 PSI to optimize rolling resistance with 38mm tires, but I could safely run less (e.g. mid 30 PSI) to maximize comfort. My gravel bike has 40mm stated tire clearance for 700c tires, but many gravel bikes these days have more clearance than that for 700c tires, and even more with 650B tires. If you are already quite low on tire pressure, you could explore changing tires.
As a side note, I am 5' 5" and I have proportionately short legs. I have a size S gravel bike, and I have only 70mm of seatpost (from the seat clamp to the seat rails). Hence, I can empathize with the issues facing shorter riders.