The first question to ask yourself is whether you're looking for something synchronous or asynchronous. You have a worldwide user base, so a scheduled event (party at UTC 20:00 or whatever) is going to be convenient for some and difficult for others. That might be ok (see below), but it's an important question to answer early in your planning.
Next, how "on-theme" do you want your celebration to be? Is the primary goal to be celebratory (in some fashion), or to do something related to your community's theme in a special way?
Next, do you see this as a one-time event or the first in a series? If you'll be having other celebrations then it might be less important if any particular one is restricted by time or location.
Here are some examples of celebrations I've seen online communities do. I've characterized them by the answers to these three questions (the third is fuzzier). These aren't specific suggestions for your community, but reports of things that have been done that might help you decide what to do for your own community.
Synchronous, partially on-theme, series: Mi Yodeya celebrated its fifth birthday with a physical gathering hosted by the founder of the site. Only a small portion of the worldwide community could attend, but perhaps next time we will have concurrent celebrations in several cities. (Your community isn't as large, I know.)
Asynchronous, on-theme, series: Pets.SE celebrated its first birthday with a contest in which people shared stories and/or photos of their pets and the community voted for their favorites. There was a small prize for the winner. We all know that the Internet is for cats, so this was popular. The post was open for contributions for a few weeks. The community repeated this for its second birthday, without the prize (I think).
Asynchronous, semi-on-theme, series: Worldbuilding.SE called for ideas to celebrate its first birthday. While it wasn't the top vote-getter, what actually happened is that we launched our blog, with contributions from several community members (particularly in the first, birthday, month). Another suggestion got twice as many votes but the community didn't follow up as much; sometimes good ideas don't actually work out.
Synchronous, on-theme, one-time: When Mi Yodeya graduated from a beta site to a full-fledged site, we had an online launch party that allowed participation in various ways. We used a radio-show format, with an actual phone number that people could call into to address the community. We had a chat room running in tandem, so people could make comments or ask questions without being on the air if they preferred that. We had a couple of guest speakers, who prepared on-theme material to present. The party also included some trivia games (again, on-theme). This didn't work well for all time zones, but to mitigate that somewhat, a recording was posted.
Asynchronous, on-theme, series: Writers.SE had a contest during National Novel-Writing Month (NaNoWriMo) to attract new content to the site. The contest ran for a month, with regular updates posted, and there were prizes. NaNoWriMo happens every year, but that was the only year the site had a big contest. The next year the site tried a lower-key NaNoWriMo topic challenge, with less success.
Asynchronous, on-theme, one-time or intermittent: The Board & Card Games site held a contest to increase and improve site content. The contest was run for six weeks around Christmas, a time that has historically been good for the site. There were small prizes. This particular contest had a one-time goal (which wasn't met, but people had fun anyway), but there's no reason such events couldn't be recurring, too.
Asynchronous, on-theme, intermittent: Content drives like the Writers contest don't need to be tied to events. Mi Yodeya held such a contest out of the blue one month, for general site-promotion. There was a small prize.
Finally, as you'll note from some of the links above, a good first step is to ask your community what they'd like to do. 1