Problem with your 'idea' is that it does not fit the context or universe of Fallout very well. Noted, you do attempt to justify that by saying that it's an "alternate dimension", but I don't believe it's an adequate excuse. If you're going to invent new rules to an existing universe you might as well think of some more and call it your own, instead of still referring to it as "fallout".
That, and it was pretty cliche. I like the idea of "you" [lone wanderer] taking over the role of "you" from another dimension, but it seems to take this idea off the Bethesda game in the series where you take over your dad's work. I do think the idea of portal technology would be interesting in the fallout universe albeit ONLY if presented correctly. Portals that are unstable, unpredictable, and with the technology generating them looking primitive and prototypical in the ram-shackle fashion that almost everything appears in within Fallout could work. Otherwise it rips off Half-Life and Stargate.
Plus, the whole "fight the evil amoral government" stuff is trite. Games are already over-saturated with this plot structure - something more original is needed.
As for my ideas: Present the Fallout universe with STALKER-esque gameplay - i.e. : Needing food, water, and not being able to take even a handful of bullets before dying. Knowing fallout, it would make the game incredibly difficult, but I feel it would better suit the universe because it would tap into more survivalist tactics in opposition to the standard "run up to well-armed bandits with nothing but an AK47 and still come out on top" scenario because you put 3 points into your 'Strength' SPECIAL skill.
It would also give more emphasis on spending points on barter and speech skills/perks which were reduced to 'dump' stats in the Bethesda game - buying food, ammunition and first aid suuplies could practically change the difficulty.
Vehicles - a new independent use of the repair skill. Could also add new gameplay elements -think of it: raider hit-squads roaming around in patched-up pre-war trucks - a new use for the 'Heavy weapons' Skill.
Rarity of ammunition - more emphasis given to provisional melee weapons - make guns more expensive/valuable.
Different strengths/weaknesses of weapons -- As you put more points into 'small guns', the base damage does not change, but the accuracy of the firearm increases; this way we can avoid the whole Bethesda bullshit of shooting someone 5 times in the face with a shotgun at point-blank range yet still not killing them. Because conventional firearms will be more plentiful, it means anyone can pick up and use them lethally, but players with experience points invested in the skill will be able to kill with greater accuracy, have bonuses to small arms repair, and reload/unjam faster.
-- Laser weapons will work opposite of conventional guns: the accuracy will always be pin-point, but the Damage done with them will become better with the points invested - bonuses to item health, reload/repair speed, etc. will be the same as the counterparts for small guns.
Note: all this done like an FPS, except for vehicle sections as a driver.