Back to the Past

Sleeping bag would be a wool blanket. There would be no practical mattress (that wasn't too heavy to carry) so I would collect natural materials for a mattress.
I wouldn't carry a stove, just cook over an open fire.
For clothing I would have a boiled wool jacket that would cut the wind and keep me warm while wet. There is no practical solution for rain gear, it would all be heavy, terrible, and only marginally waterproof.
I would learn to go barefoot. I read that Lewis and Clark resoled their moccasins every other day.

PACK-> I'm thinking balsa wood and waxed cotton

SLEEPING BAG AND "MATTRESS"-> Wool blanket

TENT-> waxed cotton

COOKWARE/STOVE-> enamelware cup/pot… cook over a campfire

SHOES-> leather I guess

CLOTHING-> waxed cotton, felted wool

PACK-> Half-bushel oil cloth knapsack, (approx 18L)

SLEEPING BAG AND "MATTRESS"-> Thick wool blanket and sleep on some nice springy browse.

TENT-> a 10'x10' cotton cloth that's been water proofed. Water proof with 10 quarts of water, 10 ounces of lime,and 4 ounces of alum. Pour the solution over the cotton cloth in a container and let stand for 12 hours. Rinse and dry. It should be water proof after that. I would have metal grommets around the perimeter with a length of cord attached to each.

COOKWARE/STOVE-> 2 quart tin pot with bail handle and lid. Cooking over open fire

SHOES-> Whatever the most comfortable Left/Right specific leather shoes I could find would be.

CLOTHING-> Clothing would probably be standard wool or other common clothing of the era. If it was raining, or looked like rain I would set up camp and start a fire.

I'll add:
TOOLS-> a double bit hatchet and pocket knife. And fishing rod.

(Most of this information was taken from "Woodcraft and Camping" by George Washington Sears a.k.a "Nessmuk" available from Amazon.)

http://www.amazon.com/Woodcraft-Camping-George-Sears-Nessmuk/dp/0486211452

or free from Project Gutenberg

http://www.gutenberg.org/ebooks/34607

A college professor told me that even into the 1850's shoes were universal until worn on the same foot for a length of time. Typically, soak in water then wear on the same foot until you had foot specific shoes (boots). Maybe he was mistaken. Old timers were tougher that we can imagine being. (IMO)

Here are my answers to a "time machine" early 1800s backpacking situation.

PACK-> single bag, drawstring top, compression corded sides and front removable top compartment/fanny pack,
*linen/cotton canvas, 50/50 weave treated with wax and whale oil "proofing"
*two flat, 1/4" thick X 1 1/4" wide hickory internal frame stays steam bent to my back contour and covered with heavy webbing to hold tehm in place.
*waistbelt of linen greycloth covering 1/2" thick felt W/ steel sliding clasp buckle and woven webbing center belt
*woven webbing shoulder adjustment straps (using steel ladder buckles) attatched to 1/2" thick linen covered felt tapered over-shoulder straps
*leather reinforcements on wear and stress points as necessary.

Tent-> 10" X10" very tightly woven COTTON light canvas W/ 12 hand stitched edge grommets, 8 linen tie-outs sewn to tarp in grid pattern. "oilcloth" treatment as in pack. Same cloth for 8' X 5' groundcloth

SLEEP SYSTEM->sewn-thru quilted silk covered goose down mummy bag W/ overlap 1/2 length button closure
Quilted (light linen W/ horsehair stuffing) 1/2" thick, 3/4 length "matress"

KITCHEN-> tin or copper Caldera Cone type "stove" W/matching copper 3 cup pot & lid

BOOTS-> individually lasted (R&L feet) over-the-ankle, lace-up

Maybe:
> 2 thin hickory walking sticks
> muslin head net and linen work gloves
> felt wide brimmed hat, "proofed" with a beeswax & whale oil mix as with tent

As you may guess I've given some thought to this setup over the years. I guess being a history teacher and Revolutionar War regimental re-enactor (drummer) is the motive.
Rev War pack top flaps were painted with red lead paint for more waterproofing.

Here's Henry David Thoreau's "gear list" from his Maine trips. 1850s. Really interesting read.

http://thoreau.eserver.org/woodsapx.html#6

This line from Nessmuk jumped off the page:

"Go light; the lighter the better, so that you have the simplest material for health, comfort and enjoyment.”

Excerpt From: George Washington Sears. “Woodcraft and Camping.”

You have put some serious thought into this Eric. Have you ever thought about creating a reenactment kit and backpacking with it? I've always had this goal to put a wool and canvas kit together and hike the sierras in the spirit of the early sierra explorers.

It wasn't much different on up to the 1960's. Some aluminum worked its way in, but the rest was iron, cotton, wool, and leather.

From Thoreau's list:

"An Indian may be hired for about one dollar and fifty cents per day, and perhaps fifty cents a week for his canoe"

Back to the OP: an interesting thought exercise.

An alcohol burner would be easy enough for local tinkers to create and reasonably high proof ethanol would be easy enough to distill from beer or wine.

My pack frame would be wood. Wooden tent poles aren't so much heavier.

I'm realizing how much our light packs, tents, bags and pads all hinge on synthetic fabrics and their waterproofing.

Prior to nylon, silk was the light-weight fabric of choice. It would work fine for down sleeping bags and down jackets.

Or carbiou hides for sleeping pad and sleeping bag/robe.

Since we're BPL, I'd stay away from waxed cotton for tents and raincoats. Stitched intestines for a hoodini.

Pack bag would be an oiled, thin, full-grain leather.