No that would not be. You really want an I7 quad mobile and 16GB of ram atleast.
Have you tried going with an I5 or equivalent AMD?
The single most important item on a laptop is a great CPU, and then you also need to keep it plugged into an AC outlet
I've personally used a e6410 with Premiere Pro CS5 with 8GB of RAM and while it does "run" Premiere Pro, it is FAR away from what I would deem a good laptop for Premiere Pro. This model is years old and the newer models do several things that help with Adobe a lot: take more RAM (16GB is much better than 8GB for PPro), drives are faster (SSDs much more common, my e6410 had a 256GB SSD and not many did back when this model was born 4 yrs ago), and as Bill already pointed out much more cable 22nm die quad core CPUs with hyperthreading (so, 8 cores available to PPro for editing).
You do not mention your workflow, but obviously editing DV would be much more acceptable on marginal hardware than trying to edit AVCHD or GoPro 4k!
I would expect a used e6410 to be worth about $250 today (street price). I really don't know why you would buy one now really? You can buy a sub-$1000 Asus and with a few modifications put together a really good "new" laptop so that may be a better option for you today.
Alright thanks everyone. This does help.
My reason for purchasing a laptop is mainly to use while traveling away from my home workstation. I didn't need it to be the fastest and best setup. I was just hoping for a cheap mobile option for the few days I'm away here and there during the month.
The footage I'm editing is always HD 1080p shot either on gopro or DSLR.