Will this be legal and possible using the G.E.C.K.?

For instance people who prefere Dogmeat over Rex could simply port Dogmeats model and skin from FO3, change his name, adjust the dialogue and be ready to go.

I think it would be great if this were possible. Personally I'd like some of the FO3 weapon models in FNV.

It's illegal.

I'm sure as hell that dogmeat's model is already in the game, as Sunny's dog looks like him already

In that case it will be easy to assign this model to Rex and name him Dogmeat. Nice

Why not only call Rex , Dogmeat? i will do that but i think Rex sound kinda Post-Apocalyptic, idk why but i just think that.

Well, it's only illegal if you decide to put it up on Nexus right?
I mean, if I were to have both the games on the PC I could mod stuff in from Fallout 3 for myself right?

It is not Technically legal to port content from one game to another. However you can do whatever you want on your own computer, you just can't post it to the public anywhere, ever.

Miaximus is correct. What you do on your own computer is up to you - just we don't want to know. You cannot take the assets of one game and use them in another, even if you own both games and those games are from the same company, if you intend to share the mod.