It could be a worn chain despite the low mileage. I used to buy cheap chains for my mtb and managed about 550 miles on each on each one and a new cassette after the third chain. Then I got a good deal on a bike and it came with a top end transmission. That just went on and on, I got over 3000 miles on the transmission. I now know (as do others on here) that money spent on chains is seldom wasted, so go 8100 (Shimano XT) or equivalent Stam. Also, the more expensive chains have special coatings and resist rust for longer.
if you want to know for certain whether it's the chain at fault, remove it and lay it on a flat surface. (I use the kitchen worktop with newspaper in between). Stretch it out and with a metal tape, measure 100 links from pin centre to pin centre. A new chain will measure 50" exactly. A worn chain will be longer. For example, if the chain is 50-3/8", the percentage length extension will be 3/8 divided by 50 = 0.0075. Times by 100 = 0.75% That is the level at which the chain should be scrapped (preferably earlier than that). Other percentages can be calculated. I tend to change mine before 0.6%. The higher the figure, the faster the chain wears away the rest of the transmission. I use a quick link to join the chain, so it makes removal and refitting so much easier than it would be using a rivet.
Worn chains are longer because the pitch is no longer 0.500" and they don't sit well in the gear teeth of the rest of your transmission. Instead of just sitting there, they slide up and down and wear away the teeth. But as this is your first chain, the cassette may not be too bad, if you are lucky. You should probably get a spare chain anyway. When you replace the chain, if the new one skips as well, then it is highly likely that the cassette is toast as well. In which case, either put the old chain back on and run it until you can't stand the skipping anymore and then replace the cassette and put your new chain on that. The ring also wears, but at a much slower rate, you should get two cassettes per ring. But that is only a rule of thumb, not one of the laws of physics!