If only my mind existed it would have to create the concept of time but nothing can be created without time, therefore solipsism is self-defeating. Shouldn't this automatically rule out solipsism?
Connecting solipsism with time is an interesting angle. I haven't encountered it before in the discussion of solipsism, which I take to be the view that only I exist or (more formally) :
Solipsism is the assertion according to which, from a theoretical view- point, there exists only one subject: that which I constitute myself - and according to which this "I" is "alone" and "unique." (Elliott Sober, 'Why Not Solipsism?', Philosophy and Phenomenological Research, Vol. 55, No. 3 (Sep., 1995), pp. 547-566 : 547.)
Your question appears to assume that at least something else really exists, apart from yourself, namely time : and if this is granted, then clearly solipsism is false, 'self-defeating'.
But there is no need for the solipsist to grant that time exists independently of her- or himself. All the solipsist is committed to, at most, is that s/he experiences thoughts, sensations, and so forth as if they were temporal - as if they were occurring in time.
Time for the solipsist is not something which exists in itself or which is inherent in reality as an objective dimension or feature. Time is nothing but a form under which the solipsist self-represents his or her experience. The solipsist's experience is such that s/he experiences thoughts, sensations and so forth as occurring temporally, e.g. one after another. But this only means that s/he experiences these things as if they were in time, it does not follow (on the contrary) that they actually are in time. The capacity or necessity for experiencing temporally, for imposing the form of time on experience, is simply a feature of the solipsist's cognitive apparatus.
Someone might argue that if there exists only one subject, i.e. the solipsist, then s/he could not be under the constraint of experiencing thoughts &c. as if they occurred in time. As unconstrained by anything else, because ex hypothesi there is nothing else, the 'temporal constraint' (as we might call it) could not apply. But there are two points in reply : (1) it may be simply a contingent fact that the solipsist experiences temporally, so that there is no temporal constraint but only the mere fact (which could be otherwise) that the solipsist does experience temporally. (2) Contrariwise, because the solipsist exists as the sole subject - because only the solipsist exists - it does not follow that the solipsist does not have a fixed or essential nature by virtue of which s/he necessarily experiences temporally even though time does not exist.
I am not endorsing solipsism, simply trying to show that it is not self-defeating in the way you have interestingly suggested.
The idea of time as a human contribution to experience rather than something objective and external to human experience derives from Kant's Critique of Pure Reason (1781/ 1787), I 'Transcendental Doctrine of Elements', Part I, §II 'On Time'. But Kant was not a solipsist.
If anything creates the Universe (my mind, my cat's mind, God, whatever), then that thing had to create time in some form, and according to your reasoning that would require time. Therefore, your argument isn't limited to solipsism, but covers many other philosophical and religious ideas.
If only my mind existed it would have to create the concept of time
You would have to create your own experience of time, yes. That's kinda what the idea of svabhava, substance, is. One problem with substantial persons, according to Indian Buddhism, is that we don't seem to be in complete control of things. I might infer that I am not substantial and did not create myself.
Buddhist philosophers have spent a lot time clarifying the nature of impermanent time, too, and often, not always, say that elements of cognition must have substance if they are to appear and disappear, in time. If they're right, then your solution to the problem of other minds is defective because time is just how it is. Not everything is created.
The question is grounded in a false assumption that creation require time. Time cannot exist without creation and vise versa.
Experientially, time is a measure of continuous change in the observed world.
Empirically, time is relative to the speed of matter in motion. From a scientific theory worldview, time began at the big bang and stops in a black hole. They are woven from the same fabric of space-time.
So regardless of how the observed world was created, it was done in such a way that renders the question incoherent.