Hey! That's definitely an option for you, and would do wonders.
I myself use an extender in my townhouse and coincidentally, it seems we're in a pretty similar situation. My modem is literally a foot from my front door in our closet (when we bought the property the previous owner had a little shelf installed on the wall in the front closet) and near there and our TV, Xbox, etc. it's blazing. In my office on the other side of the main floor about 30' away I'm pulling around 250mbps or so...I tested my speed up on our 3rd floor rooftop balcony, and the open air causes the signal to just dissipate. I get nowhere near that speed up there. So on our 2nd floor we had an extender put in to basically juice up our overall coverage, and it seems to really help.
As for when you're walking away with the signal remaining, I experience the same! Wi-Fi signals attenuate the same in any direction through the air so it doesn't technically matter if the signal is traveling vertically or horizontally. However, in practice, it seems like the signal goes farther in the horizontal direction. Perhaps as the signal is moving through more textures if it's shooting up through your home.
Either way, look into our TELUS Wi-Fi Boost or an extender!