Ok, first things first, if I was picking out traits for a character for a role playing game, for the situation you have described, these would be the attributes I would pick (some have already been mentioned and I am a bit constrained by not knowing the rules and bounds of the particular game you will be playing).

Physically tough, physically fit and trained in some form of self-defense or martial arts (if we are to assume another member of the trek group will handle the fighting parts of the trek then you could leave the self-defense/martial arts part out). Keeping in mind the usual roles for an RPG (a fighter, a healer, a thief, and so on) it would seem your character is taking the role of a healer. That said perhaps your skill set and knowledge should be focused on that aspect of your character.

Mentally tough, ready to take on the mental challenges of being flung through time into a harsh new reality (culture shock on an epic scale) as well as the mental challenges the new reality will present.

A master of improvisation. Since the technology may be older or non-existent, and the supplies from the past cannot last indefinitely, the character should be ready to improvise what is needed, like a splint for a broken bone, or a replacement knife handle, or a remedy for a stomachache, or a water filter, etc.

Good at communication, to facilitate truces between warring groups (if that is a likely scenario) or between individuals. At any rate, having good communication skills can’t hurt. This also implies an understanding of human nature and human behavior, which is also very useful.

If I understand the scenario correctly, the house takes care of her need for shelter, and the needs of food and water are being provided for her already and will not need to be addressed by the character? If not, then she also needs to be knowledgeable about horticulture (or at least have books in the home about it) and raising, foraging, and preserving her own food supply. She would also need ways to procure, purify, and store quantities of water. If we can safely assume her survival community is taking care of these needs for her (or the game master is simply ignoring these details) that is fine, but wouldn’t these skills make her a better asset to the survival community anyway?

You have mentioned thus far that the knowledge base will be your own. In my opinion, for this scenario, knowledge will be a far greater asset than any gear (tho for the short term gear could prove very useful). If you don’t already know some of the things discussed, could you add some books to your library that will survive the 40-year time span? Books on herbal medicine, home remedies, edible plants, primitive living, etc could prove worth 1,000 times their weight in gold. Given your character’s healer role, books focusing on this aspect would seem most logical.

OK, now for the confusing part. Your premise says “Jeanette is a Wilderness EMT getting ready for a wilderness expedition when she suddenly finds herself in a survival situation.” Is it ONLY the gear she has on her person that is not affected by the 40-year time span? Also, is she already on her own expedition when the time transport takes place? Because if she isn’t, I find it hard to believe that some of the gear you mention (like the knife and the AMK mountain medic, which weighs in at 7 lbs 12 oz and is 16" x 10" x 8") would REALLY be on her person at that moment. Also, are you considering just what she might have on her person? Or what she might also have in a pack she has just slung on her back? If she is just gathering up the gear, and it survives because it has been laying around her house for the past 40 years, then most of the contents of the FAK will be useless, as will other items mentioned. For now I will assume that she is either already on her own expedition, is gearing up as she is about to leave, or whatever so I don’t get too bogged down but the details ARE important. For the most part tho, things like medications, maybe adhesives, and other things prone to breaking down (like rubber and elastic mentioned earlier) that remained in the home will be useless to her. Thinking in terms of surviving 40 years just lying around, one word comes to mind: Titanium.

Assuming the gear for the expedition was stored at her house, she should still have access to any of it that survived the 40-year time span. So another thing to consider is what expedition was she going on? An expedition to, say, the jungles of Brazil would entail a whole different set of gear than would, say, an expedition to the North Pole. If your game master isn’t as detail oriented you could get by without being specific, but in terms of getting the most out of the experience you should consider this little detail.

Any chance you will need to do any bartering in the game world? If so you might consider including some simple luxuries like candy and gum and other needed items for this post-apocalyptic future that would be worth trading.

That's what I have. Sorry I could not offer more specific information like book titles and such. Hope it helps.