Hello, and welcome to the forum! He looks very bright-eyed and alert, so that's good, but you are correct that he looks a bit on the small size for a 2 month old, and if he's not gained weight in the last month or actually lost weight, and if he's not eating a ton of live insects every day, then something is definitely very wrong, as they are like little garbage disposals during their first 6 months, typically eating very little to no greens/veggies, so don't worry about that, but they usually eat between 40-60 appropriately sized live insects every single day without a problem, because they do about 85-90% of their total growth and development during their first year of life, and they need just a massive quantity of live insects every day. This isn't an uncommon issue, and the good thing is that you've come here for help early on in the problem, so you can likely get him back on track and correct the issue without any permanent damage or growth stunting.
Usually this problem with such a young baby is due to inadequate UVB lighting, meaning that either the
UVB light that you're using is totally inadequate in the first place, your
UVB light is being obstructed by something that is blocking a good portion of the
UVB light emitted by it, like a mesh tank lid or a clear plastic safety cover on the bottom of the long tube fixture (if your
UVB light is a long tube), your
UVB light to too far away from your dragon and his main Basking Spot/Platform for the
UVB light to reach him, you aren't leaving his UVB or his bright-white colored basking bulb on for a long enough photoperiod each day (should be on for at least 13-14 hours each and every day), or a combination of all of these. We can rule out that your
UVB light is too old and you haven't replaced it within an adequate time-frame because you've only had him for a month (assuming that you didn't buy a pre-owned
UVB light, lol). So can you please tell us in detail what
UVB light you are using (Brand, Wattage or Strength, and what Type of
UVB light it is, meaning is it a regular compact bulb, a coil/spiral bulb, a long, fluorescent tube, or a Mercury Vapor Bulb)?
Also, can you post a photo of his entire tank/enclosure, including the lighting, so we can see his set-up? That is usually very helpful.
What type of thermometer are you using? This is very important, so can you tell us if it's some type of stick-on thermometer, a Digital Probe Thermometer, or an Infrared Temperature Gun? And what are the temperatures of the 3 temperature zones inside his tank?
Also, what Calcium and Multivitamin supplements are you giving him? How often are you giving him each? And how do you give these 2 supplements to him?