There are some things you can do against Nasus as Teemo, they aren't a guaranteed win or counter, but they can help if you play the matchup correctly.
Playstyle:
If the Nasus builds Spectre's Cowl then you don't want to go for poke or short trades, applying small amounts of damage will let him sustain back up, instead you should try to go for extended harass to keep damaging him and keep him down.
Early on you can use your Q blind to prevent Nasus from farming with his Q, but once he gets to the point where he can run you down, you need to hold onto your Q blind until he gets right on top of you, that way you can prevent him from landing at least few of those smacks on you.
Plan ahead for him trying to run you down, once you are level 6 you can place mushrooms defensively, create a minefield of them and stay within that so that if he tries to run you down he has to go through all of them to get to you.
Additionally, if you hold onto an ammunition stack of your ultimate, you can place it down in front of you when Nasus casts whither to try to catch you.
Items:
You might find some more success by getting Blade of the Ruined King against Nasus, because the %HP damage will help later on and the active will help you kite him. Black Cleaver will also help shred his armor so your team's Marksman can damage him more effectively later.
Also if you prefer an AP build then you can go Liandry's Torment and Rylai's Crystal Scepter. Rylais will give your Q a slow in addition to the blind, and your poison will also apply a minor slow. Liandry's %HP damage will help later on when Nasus is tankier.
You may also want to buy an executioner's calling just so you can apply grievous wounds against his passive. This becomes even more important if he buy's Spectre's Cowl against you.
