There's not a lot of point to carrying a cartridge limited to low-recoil in a large, heavy gun. Just take a .30-06 or a 270 or whatever and handload it down to less recoil. Use H4895 reduced loads or Trail Boss and go as low as you want. When you're ready to put it on deer, make sure the bullet is designed for those velocities.
On the other hand, if you want to shrink the rifle so that it's no more than what's needed for a lower-recoil cartridge, bear in mind that you'll need to increase the proportion of weight to recoil energy to actually feel less recoil. If you drop your charge enough, a T3X Superlite can be made to feel low-recoil, but it's still a fairly long action. A quarter-bore or 6mm chambering with 80 grain bullets is going to feel like less recoil than a thirty caliber or larger with 180 grain or heavier bullets. You can also go shorter with a mini-action from Howa or CZ chambered in 7.62x39 or 6.5 Grendel. Those guns aren't ultra-light, but then if you want low-recoil you won't want them to be. They are fairly light, but still heavy for the amount of recoil energy the cartridges generate -- so they'll be low-recoil. The Ruger No. 1 also has a very short receiver, but weighs quite a bit. Handload light charges in the cartridge of your choice and it will be a low-recoil gun.
Also consider if you'll use an optic. Some of the optics out there weigh a lot. Boy they're nice, but they can add two pounds or more to the rifle. If you just want to lower felt recoil, get one. If by "low-recoil" you're looking for a smaller, lighter gun that won't recoil too much, then find a sight or optic that lowers your overall weight. It won't help with recoil, but if your goal is to downsize the whole rifle and not just cartridge, pay attention to the weight of optics.
Any cartridge can be low recoil if you handload it that way. Heavy guns result in less felt recoil. If you want a light-shooting minimalist cartridge you can get a little bit lighter rifle or a shorter mini bolt action. You can also get a short receiver with a single-shot.
Now if you want a gun for your daughter, you want to consider whether or not she'll carry it in the field or if someone will carry it for her. Low-recoil can be achieved by having plenty of weight, but if she will carry it, you'll want to think about downsizing the cartridge and the rifle. You'll also want to consider her size and particularly things like length of pull and whether the eye relief on any optic it has will work with her shorter length of pull (putting her eye closer to the eyepiece). Is the mount adjustable? Does it adjust far enough? Also consider whether she'll shoot off-hand, with a bipod, tripod, shooting sticks, or some other kind of rest.