Very common situation and, yes, you should change things to 2". You need to break up concrete until you find that the pipe is at least 2". You cannot put a 2" drain on a 1.5" pipe in the slab.
The problem is this...if the drain gets plugged in a shower (say you drop a washcloth or stand on the drain), there's very little leaway before it can overflow the curb in a shower...in a tub, you have probably at least 8-10", and then you have an overflow to take care of the excess water. No such thing in a shower.
Now, could you make it work - probably, but if caught during a house inspection, they could make you tear it all out AND fine you. They'd also look at everything else in the house much more critically, which could precipitate other issues. Depending on where you live, a permit for a shower could be anywhere from $10-several hundred, but then you'd know if it was done right, and be legal.
The trap should be right underneath the drain. All legal drains will be 2". Since the floor must be sloped to the drain, it often looks best and has less severe angles if you put the drain in the middle of the shower pan.
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