yep, you should absolutely negotiate. it's totally normal. if you don't negotiate, you might be leaving money on the table.
you may need to be able to back up what you're asking for, so do some research into comparable salaries in your local area. what you need isn't really relevant, the prevailing market rate for your work is. you need to stay friendly and positive, but also confident in what you are asking for, and know when to stop talking. and if they say it's not negotiable, and you're still fine with the pay, then take it!
there's some good advice here, and be sure to read the comments for more insight and ideas:
what to say when you negotiate salary