Backpacking stoves have come a long way, some of them are quite small but they are efficient, and you can have hot food & drinks in the field, a BIG PLUS on cold nights & early mornings! A small water filter is a good idea, I would choose the kind used by the guy who does the 'Adventures In Reach' videos on YouTube. I don't know his name, I just call him 'AIR' due to the title of his videos. He employs some cool field gear on his adventures, I liked his circumnavigation of Isle Royale aboard a 14' Sunfish, he's a cool guy who also takes dogs with him on many adventures.
I would avoid canned foods, unless they're in those lightweight aluminum cans that you can crush afterward and easily haul away. Freeze-dried or just plain dried foods, jerky, chocolate bars, trail mix, those are all good choices for the field. Dried soup mixes & bouillon cubes. Some sort of lightweight backpacking tent for you and the dogs. Bear spray to go with the sidearm. Lightweight synthetic clothing that's still warm at night. A small LED flashlight & bombproof headlamp really come in handy. Lighter & matches, just in case. Space blanket. Reliable compass. A good topo map of the area, protected from the elements by a large Zip-Loc bag.
I haven't done so much backpacking lately, since I live near several wilderness areas, but I did serve in the USA INF, and I have a long history of hiking and remote (vehicle) camping. Things I've always found indispensable in the field: good sturdy footgear, it doesn't have to be heavy as long as it's bulletproof. Some kind of cover: ballcap or straw hat, brimmed adventure hat, whatever, to shield your eyes from overhead glare which can be annoying. Good sunglasses on a "goon cord" (retention cord or strap). TP & lip balm, lol. A good beanie or watch cap for cold nights, and some warm gloves.
Don't forget a small camera to record your trip for posterity, and possibly to share pics with H&CL heroes, lol. I'm not the kind of guy who gets all gripped about a schedule or agenda in the field: I have a primary objective, and maybe some secondary objectives, but I definitely "wing it" in the field as I go, and I'm flexible enough to easily adapt to sudden changes in my "itinerary." As long as my preparations have been good, I can handle changes in the field, and that also gives me additional leeway or freedom to check out interesting places or things I discover along the way.
What other random tips can I offer? Ah, yes, this is a good one: applying cologne or perfume before setting out each day is a good way to enhance personal safety, since the chemical scent does NOT match any prey profile, lol. When in lion country, remember that big cats usually stalk upwind, since they don't know that our sense of smell is limited. If you keep tabs on wind direction as you go, that can help you be aware of which (leeward) quarter is the most dangerous. No lie, I hiked solo through many, many miles of mountain lion country, and it helped to know where potential danger lay in the field.
Oh, yeah, trust your dogs' sense of smell to alert you to the presence or proximity of predators, especially at night. I still remember the night three of us (technical rock climbers) brought a German Shepherd with us to an impromptu bivouac site on Stonewall Peak in the Cuyamaca Mountains of East San Diego County. In the wee hours, the dog started whining nervously, since a big cat was nearby... I immediately clapped my hands and made some other noise as I rose from my bag, knowing that it would help scare off the varmint. And it did, but the dog was very much aware of the lion's presence.
Last but not least, there are many cool places to hike or backpack in New Mexico, including the Sacramento Mountains near Cloudcroft and Timberon. To the west, you have the Gila Wilderness and multiple mountain ranges: the Mogollon Mountains, Elk Mountains, Black Range & Mimbres Mountains. I always wanted to explore the Elk Mountains, and there are numerous dirt trails, fire roads, USFS roads, etc., which traverse that whole wilderness area. Up north by Chama and the Brazos Cliffs, there are some really cool trails, but you'll want a good topo map & maybe some printed climbing guide sheets which show public access roads & trails. Hope this helps... good luck to ya! Cheers!
P.S. Whenever my friends & I pulled fast Alpine-style ascents of crags, domes & spires in the wilderness, we would copy the appropriate pages from the climbing guide(s) and stash them in large Zip-Loc bags, that way we wouldn't have to carry the book(s) en route, and the beta (or info) was safe from the elements. On a long hike like the one you're planning, every ounce counts, so if you can devise ways to shed weight, well, that means you can carry more food, water, gear, clothing, canine treats, whatever...
