Is this a Rhode Island Red?

New hampshire

She certainly comes from a red lineage.  The NH, a great red bird, was developed out the RIR a long time ago.  The fact is that hatcheries and backyard keepers have kept and bred red birds for a long time.  Most of the lines used by modern hatcheries simply have deviated from the pure, heritage, mahogany, brick shaped, genuine RIR a long time ago.  The modern red birds sold as RIR as a far cry from the true bred bird, which are very, very rare.  True New Hampshires are equally rare.  You might enjoy reading some of the BYC thread here called The Heritage Rhode Island Red Thread, by Robert Blosi. It is eye-opening, if nothing else.  I find it fascinating.  There is also a heritage NH thread too.

I've also had red sex links that following a molt, take on adult feathering that is nice, golden/red and even with just some black tips. 

In a nutshell?  She's a great red bird.  If you want like her, you might also mean you want more with her personality and egg laying ability.  Without knowing what strain she came from, that is going to be extremely difficult.   Even hatch matches takes on far different individual personalities.  If you want good red hens, most hatcheries sell them under NH, RIR, production reds, etc.   Hope you get more red hens that you enjoy.  Best wishes.

What you have is a Production Red, a hatcheries mix of many "red" breeds. Great layers. Not a New Hampshire, she has the wrong coloring. Not a RIR, again she doesn't have the right coloring. 

RIR

http://www.google.com/imgres?um=1&hl=en&sa=N&biw=1600&bih=1115&tbm=isch&tbnid=0xgLnx2DTwyLCM:&imgrefurl=http://thechickenstreet.wordpress.com/2012/01/24/chicken-nugget-the-rhode-island-red/&docid=Psg2btKnXoeFhM&imgurl=http://thechickenstreet.files.wordpress.com/2012/01/september-rir.jpg&w=2120&h=2168&ei=CafJT73KIojY2AW8_9jZCw&zoom=1&iact=hc&vpx=1032&vpy=777&dur=755&hovh=227&hovw=222&tx=136&ty=141&sig=112654841157991619983&page=1&tbnh=120&tbnw=135&start=0&ndsp=65&ved=1t:429,r:53,s:0,i:187

New Hamp

http://www.google.com/imgres?um=1&hl=en&sa=N&biw=1600&bih=1115&tbm=isch&tbnid=PqNPwJr6anGA6M:&imgrefurl=http://www.omlet.us/breeds/chickens/new%2Bhampshire%2Bred/&docid=66pslpFl2QPOWM&imgurl=http://omletcdn.co.uk/images/cache/502/600/new_hampshire_red_chickens_a_good_example_of_a_new_hampshire_black_tail_red_hen_.jpg&w=502&h=600&ei=5KbJT9HeEoTe2QXujNnZCw&zoom=1&iact=hc&vpx=892&vpy=726&dur=954&hovh=245&hovw=205&tx=102&ty=120&sig=112654841157991619983&page=2&tbnh=127&tbnw=105&start=53&ndsp=70&ved=1t:429,r:14,s:53,i:221

*not my pictures obviously :)

I agree a production red.  We have 2 and they are the funniest ones in the bunch!  

These are the original Rhode Island Reds from say 1940s. A great strain from Bill Bennett of Lakeland Gerogia.

What you have is the hatcery verision of the Rhode Island Red started in the late 1940s that went for increased egg production. They lost the deep red color and shape as egg production will take size away from this old breed. They are good layers and thier are thousands of them in the USA  The picture above may only have 300 per winter . bob

I think she's a New Hampshire Red, not a Rhode Island Red. Even hatchery production RIRs are darker red than yours. I've had both, and this looks like a New Hampshire Red to me.
 

edited to add--my RIRs and NHRs were from MMM, also. My MMM RIRs were much darker red than this, but the NHR looked just like this. Can you find out what color she was as a chick? They're very different as chicks.