The Yak-3 is not as fast as the Yak 9T, but is a bit better in the knife fight. With that being said it is still a very fast plane and it is not to be underestimated when speeds are a factor.
In terms of the dog fight, it is very dangerous. It does it all very well in terms of maneuvers. It can turn, roll, climb, and accelerate with the best of everything. Above all, I think it is a very stable platform, it is very forgiving. Its biggest downfall is its lack of firepower: the single 20mm and dual .50 cals offer minimal firepower with most of that being contributed to the lack of ammo. In a 1v1 it is fine. When in the goal is to go in and clear the skies of enemy fighter(s), you have better have countrymen along side of you or perfect aim. It simply does not have the ammo to stand too long and duke it out with enemy fighters.
It is a air to air fighter, nothing else. It does not have long legs for escort duty, it does not have abundant enough firepower to hunt and destroy bombers, it does not carry the ammo nor the ordnance to hammer ground targets. There are always exceptions to the rule, but generally speaking keep the Yak-3 as a short term knife fighter (or be able to retreat and rearm/refuel on a regular basis).