Beginner at composing - Harmonising a melody in imitation of Mozart's Klavierstück KV 33B

Question

TL, DR :
I don't know how to harmonize this melody (explained below) and need help deblocking (questions at bottom)

I have been learning violin for a few years now and I wanted to learn how to compose as well. After learning basic music theory (intervals, chords, degrees, etc...) I figured a good way to start would be to imitate easy compositions from famous composers and practice composing. https://musescore.com/user/30131964/scores/6290082

I started by the melody of the 1st part, I took a very simple motif and imitated the piece.

Then I went onto the bass line or harmony of the piece, I noticed that it started with 2 arpeggios that were decomposed chords (1, an octave above the other).

I struggled on the 1st phrase/1st bar of harmony because I go from a I to a V in the melody. (I noticed mozart had started the melody on the IV degree instead and finished on I)

Then, on the 2nd bar, following up with a chord of the 2nd degree (minor chord) sounds dissonant to me. (I noticed mozart repeated the 1st phrase)

I've been trying things for hours (in the picture below are a few of my tests), but I can't find a solution for a consonant harmony. (later in the piece, the harmony aren't chords anymore, but seem to be almost a small bass line melody)

So hear me out:
how would you go about harmonizing in this specific situation ?
or at the least,
What should I try or look at ?
What "laws of consonance" am I missing ?
Do I need to learn counterpoint or something along those lines ?

Thank you very much for reading this, and don't hesitate to talk up if something is not clear or not good !

EDIT 01: (acknowledgement)
I thank you for your answers. I didn't have allot of free time today so I will research each answer I received on my side and come back tomorrow (Europe time).

EDIT 02:
I tried both solutions proposed thank you all for the help. To @euryanthebleu; I continued with your advice and tried a few things:

I struggled on the 2nd part with the rhythm, the "phrases" were smaller and I thought it didn't work out with the old harmonic rhythm

Thank you for the advice, I didn't know about harmonic rhythm at all. I still find it hard though to have a nice harmony and a nice melody, but I now have a little more insight on it.

Answer 1

I would suggest something like this:

The problem you ran into was caused by the fact your harmonic rhythm was quicker than that used in the Mozart piece, so when you spell a d minor chord for 4 crotchet beats, the melody suggests a C major chord after 2 beats. Mozart is able to spell an F major chord for 4 crotchet beats since the melody implies the tonic triad.

In my suggestion I imply a G major chord for the first two beats of bar 2, and the go to I.

You also mention counterpoint which is important since in this piece you can see the 2 lines - melody and bass working in harmony and as two separate voices - even in homophonic textures there is voice-leading present. To imitate the style of Mozart in this type of homophonic composition you don't need to get into the nitty gritty of fugues and counterpoint, but notice that the two lines often move in thirds and sixths. These are imperfect consonances and this is good practice in this style, as you would learn in counterpoint.

Answer 2

Tried the first couple bars with my admittedly very clumsy skill and they sound kinda like this to me: C Emi / Dmi C(?) / Ami Dmi / (...) (Not sure about the end of second bar, honestly the jump from C to G feels kinda hard, I think I might put a B in the melody there instead of C and then the obvious G for the chord.)

But if you want someone to talk about theory and Roman numbers, I'm not your guy. I'm not gonna tell you why I chose Emi instead of G there. It's on the intuitive level, in the subconscious. "Sounds good to me" is all you're gonna get here.

(Nor am I saying you need to choose Emi over G. It's your tune, do whatever you want with it.)

And maybe the overthinking approach isn't quite that productive for you either. Instead of "there's a V in the melody, I absolutely must put the V chord in there!", you could try "hm, B and G, these appear in G, or Emi, or Cmaj7..." or "only prominent tone in this part is D, wonder what will work with it, G, Dmi, D7, Bmi, Bb?" (plays a couple options, decides on the right chord by the ear, builds the harmony line from that).

Don't get stuck in rules that are really more like suggestions.