I have had people stay with me short term - I just had a friend whose closing on her new closing got pushed back two weeks come and stay for that long. I had a second cousin who stayed with me for 3 months during an internship.
My place, like yours, is small. It's a one bedroom. My cousin and I shared my queen bed (good thing I wasn't dating yet then ); my friend who stayed earlier this month set up an air mattress that took up half the living room.
I understand wanting to help people. I also understand home being a sanctuary. I have another friend who heard that L stayed with me for those two weeks, and has been hinting that she'd like to crash here if she has a gap between apartments (her lease is up Aug 15 and she hasn't found a new place yet). I adore her, but I'm not going to invite her to stay. With L and my cousin both, I knew that their personalities and mine meshed, that they would understand if I ignored them and just watched tv or something, that I wouldn't need to entertain them, that they'd clean up after themselves. And they knew me well enough to understand that yes, staying with me was an imposition, but one I'd willingly accepted for a short, predetermined amount of time. This friend wouldn't get that, and would want constant validation and entertainment. I couldn't do it, and I know that, so she's not going to be staying with me - even if she directly asks.
You need to know your boundaries. Would it make you an awesome friend if you gave her a place to crash for a few weeks? Yep, but that isn't the same as being a doormat while she moves in for a year and drives you crazy or is constantly late with rent, etc.