I was wondering if someone can perhaps help with this proving. I am not sure how to handle a temporal frame that is not a set of only natural numbers. Any suggestions?
You handle this exactly the same way you would if the frame would consist of natural numbers. What have you tried? You should also be open about this being a homework question, if it is one. Is it one?
If you want to disprove it, find a valuation and a rational number q where your sentence is not true. Otherwise you show that it is true independent of the valuation.
Let's assume we want to prove it. We choose a rational number q, and assume the left side: q⊨◻◻p. Is it true that q⊨◻p? If so, then for any from q accessible world r, i.e. for any r>q we have to show that r⊨p. Can you take it from here? (Hint: The following is the wrong approach: By assumption, q⊨◻◻p. Therefore r⊨◻p. Now you are stuck.)