post the specs here, but you definetly don't need to spend thousands just to edit. Yes it will make your life easier, but with regular t3i footage, you will encounter the law of diminishing returns very quickly. For example, I went from 8gb to 16gb of ram on my computer. Yes it is a little faster in general, but not much. Even for gopro footage/similar (occasionally I will have stuff from a friends 60d), it doesn't make that big of a difference. Where I do notice it is with panoramas or hacked gh2 footage. These things push the limits of other computers, but mine can handle it fine. If you have the money, go for it, you will love it, but don't feel that you need to sell you car and buy a new 12 core mac pro to make an edit.
From what I could find from this model on newegg:
http://www.newegg.com/Product/Product.aspx?gclid=CJL-6rO9p7sCFTJo7Aodsl0Abw&Item=N82E16834256863&nm_mc=KNC-GoogleAdwords&cm_mmc=KNC-GoogleAdwords-_-pla-_-All+Laptops+%2f+Notebooks-_-N82E16834256863&ef_id=UqffPQAABJhGZkcl:20131211055244:s
You may be alright, I don't know anything about amd processors really, 4gb ram is alright, but 8 would be better. You will want to get an external hard drive (back up and storage). Also, the screen is alright, but could be better, and that will likely be the most annoying part. Getting an external monitor could help.
Lastly, if you have the cash and want a macbook pro, I am going to sell mine at the end of the semester (this weekend). PM me for details/shameless plug