First, are there any company policies against relationships with coworkers? I'm not sure how it is in the Netherlands, but in the US it ranges from the company doesn't care to rules about being in the same reporting chain to forbidding it entirely. You can consult with HR about this.
If your company forbids it, then not only should not you not mention your relationship, she probably shouldn't apply. There would likely be consequences for lying to your management.
Second, does your company offer referral bonuses? If so, you should consider referring her to the position. Sometimes, referrals get some extra weight in terms of coming in for interviews over candidates that apply cold. You may also get a bonus of some kind if she gets the job and works for long enough.
If it's not against policy, it's probably more effective to mention that you know each other and explain your relationship.
Third, you need to consider your relationship. How stable is it? If you were to end your relationship, would you both be OK seeing each other in the office nearly every day? Even if your relationship is good, would you both be OK with the drastic increase in time spent together?
Only HR can answer the first one. Only you two can answer the third.