how long does it take to get from 1000 ELO to 1600 ELO

Four to six years. In my experience, 100 increase every year. Not unless you are talented that works really hard, it would be really fast.

took me about 3.5 months to get to 1465 from 1000, so maybe 6 months to 1600 (for me atleast).

Probably 2 years

The answer depends on the player’s potential. Also, the amount of study, effectiveness of study habits, and opportunity to play and learn from stronger players all play a role.

I have charted the development of players in my area, using their OTB ratings. players with master potential should pass the 1600 level and reach 1800 within a year or two. Players who reach the expert 2000) level reach 1800 in two to three years. Strong players tend to advance by 200-300 points per year until they plateau.

after a player plateaus, further progress is possible but becomes slower and requires more and more work.

This all relates to OTB ratings. Online speed chess ratings are much less reliable and so development is less predictable. Personally, I don’t put any weight on online ratings.