I am really not sure about your reasons for starting solids and as you can see from previous posters it may not be the best thing for your baby. I would urge you to try and come at your situation from a different angle.
At such a young age starting solids will not provide many additional calories and is really about first tastes and experiences (assuming you were to ignore the advice about delaying if you are exclusively breastfeeding). Breastmilk has far more calories per oz than first baby foods and breastmilk remains the primary form of nutrition and source of calories until at least 8 months, some say a year.
Let's imagine you did get something in her and 'fill' her for a moment - you would potentially be taking away her demand for breastmilk which could have further consequences for her demand on your milk and your supply situation would deteriorate further - not to mention the fact she may not yet possess the enzymes to digest the food you are giving her satisfactorily and she may not be able to absorb the modest calories anyway.
I know I'm coming off like a nagging big sister here but I would feel awful if you made a choice that not only risked your ability to breastfeed but might cause your baby problems.
It could well be your baby seems more 'hungry' because she is going through a growth spurt. In which case more frequent feeding may be needed in order to build up your milk supply to meet her needs. You could consider offering her the first breast again when she has finished as she will get another letdown and another mini-feed that is very rich in hindmilk and will help to stimulate your supply. You could also consider pumping at the end of feeds to help increase your supply - although baby does it best if she's content to stay at the breast.
This is also a common time for teething issues to start so if she seems unsettled it could be due to that.
If you genuinely suspect supply problems then do get help and contact a lacation consultant or free helpline - there are numbers on the bf FAQ board. I really would urge to reconsider solids at this point (putting aside all the reasons why waiting is recommended). I honestly don't think it would solve your problem. You could potentially get less calories in her, affect your supply more negatively, and potentially disrupt her sleep further if she is having any issues digesting the solids (which is more likely at a young age). In my case I found sleep got worse for a bit when solids were introduced.
Have a look at the readiness for solids signs which are described on the solids board. There are various developmental indicators. What you've described doesn't sound like your baby indicating readiness.
I hope you don't mind my directness but I really don't want you to make an error that can't be unfixed