Ministry
Just to add to C.Rabbit's observations, d-tilt (and Kirby's crouch in general) are good vs Puff because of her lightness. She gets pushed far away from you if hit by a d-tilt, even if crouch cancelling, and cannot punish it. Furthermore, you can duck under Puff's SH bair depending on the elevation that they swing from. This is useful particularly because without having to worry about shield stun > wavedash in and punish, you can simply wait for them to whiff and wavedashing in > grab/d-tilt/d-smash.
I find your use of aerial hammer interesting, but also worrying. An aware opponent can react to getting hit by the hammer if they are grounded and crouch cancel or simply hit you when you are landing. Also, if they are in the air, sometimes they will recover before you and can nair you on the way down. Grounded hammer does not have a good enough hitbox to warrant throwing it out in the neutral. I only recommend using it if it will kill 100% AND if you read the opponent's approach. It is like trying to win the lottery if you just do it randomly.
If you want to play a full stock against Puff and actually end up taking hers first, you have to move a lot on the ground and eventually bait her into an unsafe aerial that you can grab or tilt. If she full jumps, sometimes you can get under her and do a rising SH bair to intercept her hurtbox geometrically. In short, you have to use your fast ground speed to check mate her repeatedly, which is difficult considering there are going to be a lot of instances where you can get cornered and have to simply shield her bair and regroup afterward.
Against Doc, you don't necessarily have to jump to avoid pills. If Doc does a high pill, you can stand behind the last bounce in highest point of the parabola, and the pill will simply jump over your head and not touch you. Obviously, you have to be careful about your spacing if you do this, because Doc might be counting on this and use it as an opportunity to pin you down. Alternatively, lower pills can be easily turnaround u-tilted through. Doc's shield pressure without pills isn't that good, so if you think Doc will approach with an aerial you can usually just shield it and shield grab/bair out of shield. Try to not let Doc roll in when cornered, because cornering Doc is not easy to do, and you will regret letting him get back to center stage.