Reading up on rogue planets (i. e. planets not orbiting a star), it turns out that a rogue Super-Earth with a sufficiently dense hydrogen atmosphere could retain its internal heat and have oceans/lakes of liquid water. What I'd like to know is whether those oceans could contain dissolved oxygen in equilibrium. Please advise if this should be best posted to Chemistry...
I'm going to say no, or at least, very unlikely. Short answer, no sunlight, no oxygen formation. Longer answer below.
A water ocean on a large Rogue planet with a thick enough atmosphere is possible, at least for while. If there's enough heat coming from the surface or under the oceans through volcanism, perhaps with it being a a younger planet with higher internal heat and more radioactive elements, and/or if the atmosphere was thick enough then liquid oceans are certainly possible. You run into problems with too think an atmosphere, because the pressure and perhaps temperature would be enormous where liquid water could form.
But if we assume somewhat Earth like, with extensive volcanic activity to maintain enough surface heat, Oxygen is more unlikely for a few reasons. The hydrogen atmosphere would prevent significant amounts of free Oxygen from ever being present and without oxygen in the atmosphere, disolved oxygen in the oceans would be temporary if it was formed there, not equilibrium.
Oxygen is also very reactive. It readily binds or reacts with all kinds of common elements like hydrogen, methane, Iron, Silicon, Magnesium, Aluminum, Sulfur and inside the Earth, trapped Oxygen wouldn't escape as a gas but it would likely bind with silicates pretty much permanently.
Oxygen in it's pure form is rare on planets because a whole lot of it needs to be produced before it's abundant enough to begin collecting in the atmosphere (or in liquid form if the planet is cold enough . . . but that's not relevant with a liquid water question). Photosynthesis is a great way to produce Oxygen from water and CO2 but it only works with sunlight as the process is very energy intensive. On a rogue planet without sunlight, I can't think of any way to produce any statistically relevant amounts of oxygen inside the oceans.
Plants on Earth produce oxygen in abundance because of free energy from sunlight and easy access to CO2 and H2O, but without all that free energy, I don't see it happening.
Extremophiles come in may types, so I don't want to say it's impossible, but life that we know of relies on chemical energy and the laws of chemical energy are pretty straight forward and the production of free oxygen as a by product is difficult without a significant supply of energy.
Extremophiles, loosely speaking, eek out a living on not very abundant chemicals from volcanic gas escaping into the ocean floor or in other difficult situations. There's many different kinds and more possibilities if you factor in Astrobiology theories, but I have a tough time seeing a method where oxygen is released. There's plenty of heat in ocean vents, but heat isn't easily converted into usable energy by bacteria. Chemical energy and exothermic chemical reactions to create stored energy, or photosynthesis is generally how the life we know creates and stores it's energy. The chemical energy required to release oxygen in significant amounts seems very impractical without significant sunlight.
Now, granted, the biology and chemistry behind what extremophiles can produce, gets pretty complicated and is closer to biology and perhaps chemistry than astronomy (though some might say astrobiology is part of astronomy), but in addition to that, exploring what chemical processes might be possible would get very long and above my paygrade so, there's a chance it's possible, but I feel pretty confident in saying your scenario is unlikely.
If it has internal heat and that the main source of energy in the ocean, then it won't ever be in equilibrium. The internal heat must slowly decrease anyway and the ocean will be warmed from the bottom, setting up a bottom-to-top circulation. It would be a bit like a giant pot on a stove.
But in principle any body of water can have a dissolved oxygen content.
I don't know how the circulation of water would affect it.