I also have a hypoactive thyroid and have for years. Taking replacement levo will almost certainly help your symptoms within a few weeks of your finding the right dosage. You'll need to get tested fairly frequently, as others mentioned, but a little stick every three to six months is nothing compared to feeling like you're sleepwalking through each day despite sleeping twelve hours a night.
If it helps to know, I've had a hypoactive thyroid since my early 20s and am now 41. I was able to lose over 70 pounds in my mid-20s, so a hypoactive thyroid that's controlled with medication is no impediment to weight loss. It took me about eight months to lose it all, so it was quite quick despite my bum thyroid.
On the flip side, once I started working a desk job I also packed on the pounds WAY more easily than I could've imagined, so yeah, those of us whose thyroid hormone levels are on the low side of normal even with medication do have to watch that.
But hey, we're already watching that or we wouldn't be here, right?