Would giving free 1-year subscription for early signups advisable?

I advise against it for the following reasons:

1. You want to determine whether customers will pay -- as early as possible. The worst case scenario -- even worse than not having users -- is that you serve users on the free tier for a year and learn only after the year is up that none of them will pay for the actual service. It would be better to find out early whether they're willing to pay.
2. In addition to figuring out their willingness to pay, you want to figure out what price they will pay, and what model works for them (e.g., subscription pricing, usage-based pricing, etc.) The only way to learn that is to ask users to pay that amount early.
3. You communicate that you don't think your product is worth much. Users who would be willing to pay may go for a competitor instead because they think you're an amateur.
4. If you attract users who want a free product, you'll get feedback from them instead of users who are willing to pay, and you'll end up building features for them instead of features for users who would pay. Basically you'll dig yourself further into a whole over time by listening to their feedback.

Instead, think about what is the moment when users will get the value of your product. For example, since you're doing performance monitoring, perhaps there is a moment when you show users their first site outage. That could be an "aha" moment when users see why your product is valuable. Or alternatively, maybe that "aha" moment is after they see 1 month of daily emails from you showing that there are no outages on your site. That would be a good time to charge.

from my point of view, it's too "generous". I think that 3 free months is more than enough to attract some leads. However, I don't know the overall landscape of your situation but I consider this strategy too expensive.

Have you estimated how much it will cost you?
Are you able/willing to afford it?