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Yes! It sounds totally normal, and a routine will slowly start to develop. That is amazing sleep for such a little one, she has to tank up! Just keep nursing whenever she wants, at this age she is still trying to establish your supply.
Kellymom.com has a lot of resources that were very comforting when my daughter was that little.

Yep. DD used to eat every hour but started spacing them out more around two months. By 3-3.5 months she was down to eating every 2.5-3 hours.

Yeah. I mean, my 28 month old just stopped nursing.

Kidding. Kind of.

My baby nursed for 6+ hours a day until at least 6 months. Then it was 5 hours, then four. She was always a slow and long duration nurser. I could have cut the time down earlier than I did, but when she was young and still only nursing, it was just a matter of going with the flow.

@Pirouette: holy cow! We didn't get 7-8 hour stretches until like... 8 months Definitely keep it in perspective, she HAS to eat that often to sleep that long!

I could have written this in my LO's early newborn stage. I swear she nursed every 45 minutes all day long for a good 3 months. I was constantly questioning myself and wondering if I was doing something wrong or if something was wrong with her- maybe supply issues, maybe reflux, etc. to make matters worse, all our family and friends had never even heard of cluster feeding and were in shock that she was always constantly nursing. i called tons of LC's and went to breastfeeding support groups and they always reassured me that it was totally normal and some babies just like to cluster feed! i remember not even being able to leave the house or couch some days because it seemed like we were always in a never ending growth spurt. around 3 months her feedings started to space out a bit more, maybe even earlier than 3 months. then we got into more of a routine and "schedule" which was so much better. so hang in there mama! i know how hard it is, but it is all totally normal!!!

C was like that for the first several weeks (minus the STTN ). I'm sorry I can't remember when it spaced out, but it did gradually, on her own. We still sort of cluster feed at night to tank her up for her first stretch of sleep, at 6 months, but I actually do it intentionally (like she eats at 5/5:30 and again at 7). Otherwise it's about every 3 hours now, but she can go longer if she's napping or distracted.

In those early, nonstop nursing days, I just kept repeating to myself "This is establishing your supply. It's short term difficulty for long term breastfeeding." I don't even know if that's totally true but it helped me deal with it. That, and Netflix streaming and On Demand. I watched the entire series of Parenthood while nursing.

@Pirouette: haha, my family was the same way- drove me nuts! i even did a weighed feed to see if it was indeed my supply, and she got over 4 ounces in less than 10 mins! these 2 articles helped me a lot during this time:
http://kellymom.com/bf/normal/growth-spurts/
http://kellymom.com/parenting/parenting-faq/fussy-evening/

you are doing everything right and it will pass soon enough!