I have been going out with a girl for six months. She has been counting months (she will send me a text telling me how many months it’s been almost every month). I want to do something for her, but I have no idea what.
I am please asking for your humble opinion, but I really don’t want your opinion if it is “do nothing, it’s only six months! How are you going to top it every six months?!” or anything inappropriate.
Either make her dinner, or take her to a decent restaurant (within your budget)–one she likes, maybe one where you took her early in the relationship. Doesn’t have to be some huge elaborate thing. Women tend to appreciate effort/thoughtfulness.
Make it something simple, but something that shows you know her and what she’s into. For example, if she has a favorite author, get her one of his or her books in a nice hardback. Anything that shows you have listened to her will go over well.
I’ve edited your title to make it a little more specific about what you’re asking. 
Agreed. This is harder with some people than others, though.
You could just make her a really nice home-made card, and perhaps also give/make her a really nice box to keep that and any other similar things in. This will only work if you’re the type to be a bit romantic and give occasional mementoes, cute notes left in her handbag, that sort of thing. I know a lot of dopers would loathe that but my GF loves it - I bought a vintage US-style mail box to use as the box, but that probably works better outside the US.
Something to do with “six” might also be nice. A necklace with six nice pearls on it, for example, to be added to later (this can look good if the chain’s also pretty).
I agree with this. Most women just want to feel like you care, and it truly is the thought that counts. I feel like this is one of the few areas where we’re simpler than men.
Here’s an example - I share a birthday with my boyfriend’s mother who lives in a different state. I’ve told my boyfriend repeatedly that he didn’t need to get me a gift, it really isn’t important to me. Apparently you guys just can’t accept that as fact. His mother has told him the same thing, and all she wanted was a card with a nice note from him. She sends him cards all the time, probably a couple times a month. On our shared birthday he had sent her a gift but no card, so she got upset with him. I just wanted him to come to dinner with me and my family, and I’d timed it so that he had time to make it after work. When he told me he was running late and didn’t think he’d make it on time I got upset and we fought. He was running late because he was buying me a gift. That upset me because I’d told him I didn’t want a gift, I just wanted him to be there at dinner.
Moral of the story is that you’ll make her happy by listening to her and showing her that you pay attention, and that she’d rather have your time and effort than your money. I know this doesn’t apply to all women, some women would rather just get your money and have you leave them alone. But most women that really care would rather you do something special with your time together. I suggest that you find something to do together and make a memorable experience. You don’t have to spend a lot of money to do so. I don’t keep track of dates, but if you think that’s something that is important to her then mention it before she says something to you. She’ll be happy that you cared enough to keep it in mind.