A quarter grain is a very conservative dose, but I could be more specific if you post the lab work that led to her decision (with reference ranges from your own lab report, please).
"She is also waiting 6 weeks to recheck and then only doing TSH as she says I don't need the T3 and T4 checked anymore since surgery." Six weeks is too long when actively adjusting meds. Four weeks is plenty of time. She's dead wrong about just testing TSH. You need all three tests every time you have lab work to manage meds effectively. The red flags, bells and whistles are all going off saying this doctor doesn't know a lot about thyroid.
The thyroid is the organ that uses most of the iodine we require. It's used in other places, but once your thyroid is removed, your required intake is going to be much lower. Of course, you get some iodine from diet. Perhaps your doctor feels your dietary intake will be sufficient at this point?
TSH 4.8
T-3 FREE 2.5
T-4 FREE 0.9
Please post the reference ranges for FT3 and FT4. Ranges vary lab to lab, so they have to come from your own lab report so we can see where you fall in the range.
T- Free 2.3 - 4.2
T-4 Free 0.08 - 1.8
So, you can see that your FT4 is low. It's at 10% of range, and 50% is the guideline. Of course, 50% is only where many of us have to be to be symptom free; we each have to find our best level. Also, due to the high T3 content in desiccated, it can be hard to achieve 50% without overdoing FT3 levels.
However, your FT3 is also very low. It's 11% of range and the guideline here is upper half to upper third of range.
I think you should ask about an increase. Nudge your levels up a little slowly and see if you feel better.