She was made Empress of India many years after the Great Famine (1876). Of course she had some influence over political matters but not a huge amount. Equally, of course, the British response to the famine was very poor: Trevelyan was the tip of an iceberg of prejudice which viewed the Irish as a superstitious, feckless people who had it (the famine) coming. Nonetheless, it's also the case that there were national and local collections on the mainland for relief.
Could more have been done at government level? Certainly. Did Victoria sit in Windsor rubbing her hands in glee at the plight of the Irish, instructing the government in its approach? Nonsense.
Yes I'd largely agree with all of this.
There are crucial dates which may help give some understanding.
Victoria was born in 1819, came to the throne before she was even 20 in 1837, the Irish famine started in 1845, she would only be a relatively young Queen in her twenties still unsure of herself and very reliant on her prime minister's for advice on how she should act.
The electorate in Britain was only a relatively small percentage of the male population. The reform bill of 1834? had widened the franchise slightly and got rid of the tiny so called 'rotten' boroughs who could return MP's with a miniscule electorate while whole cities went unrepresented. So abolishing tiny districts, gave representation to cities, gave the vote to small landowners, tenant farmers, and shopkeepers and to householders who paid a yearly rental of £10 or more and some lodgers.
This matters because the governments of the day largely only had to look after the interests of the landed classes, and with MP's outside the cabinet, unpaid, the parties themselves were made up of the very rich who could afford to live without a salary and on their other income including inherited wealth, land and rents from tenant farmers.
Even in good times the poor at home were not given any consideration, living in absolute poverty and earning a pittance for hard work, it was a time where the wealth of the nation and its influence abroad through empire were largely paramount.
Given then that the poor in England were treated so badly, the possessions throughout the world were also only there for the wealth and strategic value they could provide for Britain often in extending it's influence and territory even further, they were never interested in the actual indiginous populations.
It's against this background that the government of the day would have no real interest in the Irish peasants helpless plight at the best of times, they were only interested in suppression and taking what they could.
Governments being made up of the wealthy and landed, that's Liberals as well as Tories would protect their own classes interests and not particularly the the majority of the populatiin (the Liberals ruled for most of her reign, although Lord Palmerston, Lord Melbourne (a Whig, predecessor of the Liberal party) and later notably Peel and Disraeli weren't.) Peel was a conservative who broke away from the party over protectionism (he was against it) forming his own Peelite party.
The prime minister (Robert Peel) may well have advised Victoria, she being so new and unsure, on any size of contribution and kept it very meagre, suppression of the poor helpless and destitute being very common at that period. The poor laws and workhouse were features of that century's laws, this isn't an environment we recognise today so easily.
Finally, the queen although having only a constitutional power could talk to her prime minister, and her government - far closer to the aristocracy than we have today, would more than likely take her views in board as they may very well coincide with their own.
Victoria had no actual power and was only s constitutional monarch but often had sympathetic prime ministers who would very much be inclined to take her views into account. At the time the famine started she was 25 or 26 and almost certainly dependant on her government for any amount, or reduction of that amount, given.