Baby 1/2 dwarf bunny is sick

Question
I got a baby female dwarf bunny 2 days ago. She is aboutr 6 weeks old. She has always been very mellow but even when she first got home she would hop around a little bit and was enjoying carrot sticks I was giving her. Now it seems like all she does is lay down...not really eating or drinking and she has a stuffy nose I think. She won't even take a carrot stick. She sits and occasionally falls over and lays on her side. Can't afford a vet bill right now...is she going to be ok? What can I do?

Answer
There are two things that strike me here.  

If your rabbit does have a stuffy nose, many things can cause that.  This site addresses those:
http://www.bio.miami.edu/hare/sneezing.html

The stuffy nose problem really should be addressed by a vet.  Some of the causes of stuffy nose can get quite serious if left un-treated.  It might be possible that you could find a vet willing to work with you in terms of payment.  It is quite likely you may have difficulty in finding someone to do that, but it can't hurt to call around.

The other issue is diet.  The lethargy and lack of food or water intake would be a response to a issue in the diet.  Rabbits digestive systems are very delicate and a problem in diet can lead to some of the symptoms you describe.  

You mention giving your rabbit carrot sticks.  Vegetables at your rabbit's age may be upsetting the balance in your rabbit's system.  At this age, a rabbit should be getting a high fiber alfalfa pellet and hay.  Really not much more is needed at that age.  This site gives dietary information throughout a rabbit's life span.  I use this page as the foundation for all my rabbits:
http://www.rabbit.org/faq/sections/diet.html

Right now, I would make sure he gets a quality hay and pellet.

However, your problem gets a little more troublesome because you mention that your rabbit is not eating or drinking.  This can get get quite serious.  Unfortunately, the best response for this is to see a vet.  If there is a digestive problem the vet can diagnose and treat that.  These site have more info on digestive problems including syringe feeding.  
http://www.mybunny.org/info/gi_stasis.htm
http://www.bio.miami.edu/hare/ileus.html

I don't want to sound all doom and gloom, especially when you can't see a vet right now.  If you go on the assumption that it is dietary problem, you might be able to nurse your rabbit through digestive problems.  But I really do think you should take your rabbit in to see a vet.

These site give a list of vets:
http://www.rabbit.org/vets/vets.html
http://homepage.mac.com/mattocks/morfz/PB_vets.html

best wishes for your bun