lacking in leg strength and stamina exercises?

hello all

I am a new rider, about 4 months now, 44 years old, male, 72 kg (165
pounds?) , riding on weekends only. Riding for fun and fitness only. I have
a Trek 1000 road bike (2004) and Shimano clipless pedals (M540).

I find that I can pedal relatively well at cadence of 90-100 rpm but if I
have to push a big gear then I very quickly run out of steam. I also have no
stamina and have to stop for a drink every 15 min of so.....

I am wondering what I can do to improve my leg muscle (quads?) strength and
general cycling stamina without ruining my knees and other parts of my body.
Perhaps some easy to do at-home exercises? I heard step-ups are good but I
have no idea what they are exactly....

thanks in advance

--
Yuri