I'm not being contrary just for the sake of contrariness, but I do have a different perspective from all the other posters as well as a departure from the advice I normally give in this situation.
First of all, the mere act of applying for another position looks neither good nor bad from a resume perspective. You don't list all the jobs you've applied for, you list what you've done. If you apply for a job with me and you show ten years of experience, I don't know if you've applied for a new job on a weekly basis in all that time or not, and frankly I don't care.
While you don't say if the opportunities in question are in the public or private sector, unlike another poster I'm assuming they're public since they were brought to your attention by another government worker. I'm a government worker myself (Federal) having spent more than 30 years in the private sector, and I can tell you that job hopping in the public sector is much different...it's a lot more accepted and expected, mostly because administrations change so frequently. Washington DC is a very transient town for that reason. Don't let that hold you back.
You are correct, however, to be a little concerned that it might get back to your current employer that you're applying for another job. There are no secrets in government service, it's a remarkably tight knit community and something I've found very disconcerting considering my own background. That really doesn't matter too much either for the same reason...folks in the public sector routinely job hop. Only you can figure out what kind of relationship you have with your boss and whether or not...and how...an unsuccessful application for another position will affect that relationship.
There are just as many good and bad managers and situations on the public side as the private, so that's not a consideration. You do ultimately have to decide what makes you happy. What's your own personal Maslow's Hierarchy of Needs? Figure that out first and you'll have a better idea what to do.
BTW, it's not necessarily true that the private sector is less secure and comfortable than the public side. Every single one of us should come to work every single day expecting to hear the words "you're fired". The government is just as fickle an employer as any publicly traded or privately owned company, and that's a good thing...never allow yourself to get complacent, and never allow yourself to get so deeply ensconced in a womb-like comfort zone that you're afraid to make any moves. Without risk you don't make mistakes, and without mistakes you cheat yourself of a learning opportunity.
To answer your specific question...no, it doesn't hurt to apply. You have very little to lose and potentially much to gain.