The subjunctive mood is preferred in Latin America when it comes to the conditional form (see last paragraph here). According to the Nueva Gramática de la Lengua Española (see §23.15u), this alternation is common with the verbs deber, querer and poder1: "Debieras~deberías prestar más atención" or "Quisiera~querría que la conocieras". The versions with the conditional forms are more common in Spain, and those with the subjunctive form are more common in Latin America. Of course, the use of the subjunctive instead of the conditional form is rare when the verb is part of an apodosis.
Therefore, in Latin America we can say:
No estoy seguro si debiera/debiese desayunar. (comer el desayuno sounds a bit redundant because breakfast is obviously eaten.)
And in Spain, you will hear:
No estoy seguro (de)2 si debería desayunar.
However, when you want to replicate what's been said to you, you can use the conditional, both in Latin America and in Spain:
— Deberías desayunar.
— No estoy seguro si debería desayunar.
1: This applies to simple forms. Unfortunately, the rules aren't that clear-cut for compound forms. Some examples from the same source with compound forms are "No sé cómo hubiera~habría acabado eso" or "Te hubiera~habría decepcionado". As you can see, the rules for alternation between the subjunctive and the conditional forms are less restrictive with compound forms, for which it can occur with a wide range of verbs ("acabar" or "decepcionar" in the examples) and situations. The Latin America/Spain difference also applies here.
2: The version without the preposition (de) is common in some regions, but would be considered a form of queísmo (press Ctrl + f and type "seguros" for an example from an authoritative source).