How soon can pregnancy be detected with a HPT?

I don't have regular periods so I can't use my last period as an indicator. My doctor told me I'm 8 weeks pregnancy and conceived around January 26th. I also had two ultrasounds in the last two weeks that showed I am 8 weeks. But I took a pregnancy test on February 2nd (a regular test, not an early detection test) and had a very faint positive. Is it possible to detect pregnancy so soon after conception or is my doctor wrong?